"Dry" Spots After Oiling Rosewood Skovby Dining Table  

The oil in rosewood has anti-oxidants in it. Dying oil finishes dry through oxidation. The result of this is that drying oil does not dry on rosewood.
I suspect that in front of the chairs the finish has been worn off from use, leading to cracking veneer, and to areas where the your oil is not drying, so after a time it evaporates, and/or is rubbed off from use. Leaving it looking dry again.
Rosewood should not be directly finished with an oil finish for this reason. It should be first finished with de-waxed shellac for a few coats, buffed with 0000 steel wool between coats. Then it can be oil finished. Zinsser makes a pre mixed shellac that is readily available in the USA.
Oh, and the thinner Zinsser uses is like 50% drinking alcohol and 50% methyl alcohol which is the stuff in moonshine that makes you go blind and die. So it has the fine great smell of an incredibly stiff, yet deadly drink. If you prefer it not deadly, you can get the really high proof grain alcohol, and de-waxed shellac flakes and mix your own.

While I have only refinished Rosewood a handful of times, I have had similar issues, like you described, in the past with table tops in other woods.
This happened to me back when I first started refinishing furniture(primarily teak), and mainly on table tops that were veneered. What I found to be the issue was my fear of burning through the veneer when sanding, coupled with not understanding 'how far to sand.'
The original factory finishes on a lot of these "oiled" tables, seemed to have a bit more film build than you can get with typical Danish Oil applications (I suspect that there was a higher varnish content in the factory formulated "oils").
So, in the areas that were well used, over many years, the finish gets worn off. When you are sanding the top, fear of burn through often leads a person to 'under-sand.' So, you end up with areas where the finish was completely removed, down to bare wood (the high traffic areas), and other areas where the original finish was just 'smoothed-out.' This results in blotchiness of the sheen, where the DO penetrates deeply in the bare wood spots (more matte). But, in the areas where there was still finish, it does not penetrate as deeply, and basically builds upon the original finish that is still there (increased gloss).
I found that I could usually remedy the sheen issues, by applying a few coats of a film-building wiping varnish, after the oil has fully dried. I usually formulate my own wiping varnish at this point, but General Finish Arm-R-Seal (Satin) is pretty good for table tops, since it cures pretty hard and seems to have a a much higher quality natural resin formulation than your basic minwax poly. As long as you don't go crazy with the varnish, you will still get a finish that is close to the wood (and far more protective than oil alone).
Over time I have learned that if you are going to sand, you need to be deliberate in your intentions. It either needs to be to smooth the existing finish, or to remove the finish completely. Mid Century veneers, tend to be much thicker than modern day veneers, and again, if you are very observant and pay attention to what you are doing, it is rare that you will sand through. Now a days, I always go for removing all of the finish, and starting from bare wood. You have more control over the whole process this way.
Leif's description is also certainly plausible. Using shellac seal coat(s) is always advised, on any wood, as the first step to the actual finishing process. It seals the wood, which promotes uniform penetration, keeps the natural oils in the wood, and helps make your finish coat(s) far more even. Again, I usually cot my own shellac, but the de-waxed Zinser Seal Coat isn't too bad.

Thanks for the help Leif, having scoured forums for insights on refinishing this table, this is the first time I've seen this type of feedback about rosewood. Almost everything I've seen said "sand, oil, wax" but I may have just been looking in the wrong places. That being said, I have a few more questions that I hope you can help with.
What exactly does the de-waxed shellac do to the wood?
How would you recommend I move forward with Zinsser? 90% of the table looks great, do I need to re-do everything or can this method be used just on the trouble spots? I'd like to avoid sanding where possible since it is a veneer, does the recently oiled finish need to be resanded?
I see you said that after wiping with the Zinsser you can then do an oil finish. Will this method change the outcome of the oil finish?
The detail in your response sounds exactly like what I am seeing. Would you say that the issues are definitely not because of greases in the wood?

Shellac's solvent is denatured alcohol. Shellac and DNA penetrate better than most other finishes. The Shellac will seal deeper into the wood, but also fill the areas of the wood that are more porous than other areas. So, when you start laying down other finishes, they wont absorb/penetrate unevenly. Shellac also will seal the natural oils into the wood, and create a barrier between these oils and your finish. Shellac hardens entirely on solvent evaporation, not oxidation reactions. But you can really only use the seal coat with the bare wood, at the start.
If I were you, I would try a wiping varnish (satin) first, to see if you can even the sheen with that. You should really not require more than 2-3 coats to even the sheen. lightly sand with 400 between coats, and use a tack rag to remove the dust. There is lots of good how-to videos and articles on using wiping varnish. If it doesn't work, strip and start over.
If you don't want to try the varnish, you will need to strip/sand back to bare wood, and start all over with Shellac, and then oil . Or live with what you currently have,...

Thanks for the additional info Zephyr.
Would using a wiping varnish help "seal" the wood similarly to the shellac? If I followed your recommendation to try this first, should I apply to the whole table top or just the troubled areas? Any risk of discoloration or anything between the oiled and troubled spots?
If it doesn't work and I need to strip and start over, any tips on gauging safe/even sanding depth? Like I mentioned in the OP, I only hand sanded with 220 then 320 to start with. Should I be more aggressive?
Thanks for the help!!

You can use shellac over oil. It sticks to most everything, and most everything sticks to it.

A wiping varnish seals the wood, but differently than shellac. A varnish is a surface film-building finish. If you are interested in understanding more about what these finishes are, and the differences take a look here:
https://www.youtube.com/watch?v=pCzblO0f8P8
Shellac is used to penetrate the wood and seal from within, so-to-speak. Shellac also builds a film when used as a top coat, but that is a different discussion. Sealing the wood from within, like Shellac does, is no longer an option for you, since you have all that finish already applied.
Danish Oil is a mixture of oil (usually BLO), varnish, and mineral spirits. DO is weighted more towards the oil and mineral spirits side of the mixture. Wiping varnishes are the same mixture, typically, but are weighted more towards the varnish and mineral spirits side.
If you apply a varnish, you would want to do it to the whole top, in one shot, with a nice even coat. Your first 1-2 coats are likely going to soak-in, kinda like oil would, but by the 3 and 4 the you should have an even surface sheen. Once you have 3-4 coats on, you can 0000 steel wool to knock the shine down, or polish to increase shine. You sill minimize any dust nibs, if you sand with 400 between coats, but make sure the coats are cured (24-48 hours @70F and normal humidity). There is a lot of good resources out there that will walk you through this process step-by-step.
If you want to start everything over, you have to make sure you get all the finish off. Typically, I will start with 150 or 180 on DA sander when stripping fully-intact finishes (also depends on thickness of the finish). I use this grit to remove the finish only, and as soon as I start getting to wood I switch to 220. You can tell that you are mainly removing finish, because the dust will be more white, vs. the point when you actually hit wood, then the sanding dust is wood colored. It can be quite difficult sometimes to tell if you have got all the finish off. You can somtimes see where it is wood vs finish, by wiping the surface with a solvent, but you risk gumming up your sand paper if you start sanding again too soon.
Once I have gone over everything with the DA - 220, then I switch to 220 by hand (sand with the grain!), and then 320- by hand (and so on, if I am going glossy). Use a sanding block. If you are oiling, you typically don't want to go past 320, as then the surface starts to get so finely honed, that oil wont penetrate as well anymore. It sounds like you got the oiling part down though.

I just have to say the amount of expertise available on this forum is really a privilege to experience. More than once I have been saved or aided through direct advice of info gleaned off older posts. And I'm not just saying that because I'm in tipsy holiday mode.

Unless I am misunderstanding the OP's information, then the Danish Oil is not drying in certain places, and it can be wiped off well after it should have dried. Danish oil dries by oxidation in air. And it will dry on old lacquer and oil finish. So even if the old finish was not removed in certain spots, the Danish oil would dry there. (It is entirely possible that such a spot would LOOK different compared to another spot where the old finish had been completely removed, but it should not have wet oil on top of it after sufficeint time.)
So the cause of wet oil would have to be the antioxidants in the rosewood oil. And I confess I am surprised that there is still sufficient oil in the veneer to cause problems, but what do I know?
Concretely, my recommendation would be to put a few coats of de-waxed shellac on the table as it is. Use 0000 steel wool between coats to remove any streaks. (And wipe it down really well first, then apply shellac.) The shellac will put down a very good barrier on top of what is already there. Then you can apply some more Danish Oil (or perhaps try Formby's tung oil finish).
If this fixes the problem, then great. If it does not, then the problem is underneath the shellac and I would recommend you remove everything, and start with shellac then oil.
For what it is worth, I am not a big fan of Watco's Danish oil because it seems to stay greasy/waxy feeling for days longer than Watco Teak oil or Tung oil finish (either Watco or Formby's), so I use them instead.

maybe dagonpaul can clarify that.
As I read it, the oil was drying in the worn spots, there just was not an appreciable amount of absorption when applied; it would just pool on top until wiped off. There was not absorption of the oil during the 30min period that it was left on the surface of the wood. I would expect that absorption had stopped if it had been oiled numerous times, so I did not key in on that fact too closely. It sounds like the spots are drying just fine after being wiped.
I just can't see something as thin as veneer, and as old as a mid-century table retaining enough natural oil to fully retard oxidation of BLO, especially in areas were the original finish was worn thin. In my past experience (typically when it is far too cold), a slow curing DO will get really thick and gummy, and overly shiny, not dull.
Regardless, putting down a few coats of shellac as Leif described, is an option at this point, and probably the fastest way to move forward. You just need to make sure that all previous oil applications are fully dried and cured, so there is something solid for the shellac to adhere to.
When applying the shellac, move quick, and don't back brush too much. Shellac dries very quickly, and once it starts to get tacky, going back over it, will create streaks and brush strokes. If you notice the brush "grabbing" then the shellac is already too dry to be back-brushing. If it relatively warm and dry where you are, you can re-coat within 2 hours, hence this being the fastest way forward.
Even if it is not the way I personally would go, Leif is pretty damn knowledgeable, and I have to believe that he has some idea of what he is talking about...

Don't give me too much benefit of the doubt. It is free advice after all, and I am just as crazy as the next cuckoo in the nest.
And some clarification would be good.
If the DO is fully dry after the proper amount of time, then it is a problem below, and the best way forward would be to remove it all first.
I have to assume that my shellac application technique is wretched as I can't help but get streaks. I have found that it is not difficult to erase the streaks with 0000 steel wool between coats.

Sometimes it's just impossible to really know what's going on in these kinds of situations. The problem areas might well have been contaminated by some unknown cleaning product. I'm also suspicious about the OP's application protocol and freshness of Watco. In hindsight, the table probably should have been stripped first with methylene chloride, IMO.

Thanks Leif and Zephyr for all the recommendations. I'll try to clarify what is happening.
There are two areas right in front of seats that prior to re-finishing had started to appear dryer than the rest (no sheen and small cracks in the veneer). I sanded the whole table down with 220/320 then started applying/wiping (new) danish oil in 30-60 minute intervals. After wiping off the last coat, everything looked mostly even with only a slight hint of the trouble areas visible. I finished with a paste wax about 72 hours later.
Over the course of the next week the two trouble areas started looking very dry again. I then spot sanded those areas with 000 steel wool to get through the wax and re-applied oil. This time, none of the oil soaked in, it just remains on top. When wiped, it looks as if no oil was applied to the area.
Hope this helps, thanks so much for the guidance so far.

Not to butt in, but...
Watco can get weird, even when unopened, after sitting for too long on the shelf. Often, this means it just takes longer to "dry".
Protocol for Watco application is to flood the surface, wait 15 minutes, wipe off everything that will come off, then wait 72 hours before additional application. I believe this is so instructed right on the can.
It really sounds to me like the problem areas had suffered damage, possibly from heat, and that some unknown product(s) had been applied in attempt to repair. If so, sanding may not be adequate to prepare the area for subsequent refinishing.