Selig Z chair- wood ID?  

These are birch or beech and...
These are birch or beech and use a tinted lacquer to get the walnut-esque color. Can't help you with a quick-fix for your situation, however; I had a similar issue and ended up stripping the chair down to bare wood only to discover it's birch and consequently a pain in the rear to stain evenly.

Without
finding the spot you worked on, in your photos, I can say that it sounds as if the film finish on the chair has worn through in places -- lower legs would be likely to have this condition. The finish coat(s) -- which have yellowed -- would have been applied over (most likely) stained walnut. The spotty result of your efforts would be due to the stain in your product having little effect where the clear finish exists, while in the raw spots that stain would immediately darken the wood.

Thanks.
So it's either beech/birch or walnut, then? And definitely not teak?
Glad I'm not the only one who's tried this. Still, a little obsessed with "fixing" my mistake and making this thing shine again.
The question is: Should I attempt to fix this myself or seek out a pro? Leaning toward the latter :/

strip, sand, and tint
You are going to have to strip the coating off and sand then respray with a aniline dye to get the walnut color. Good luck!

I'd say it's stained beech....
I'd say it's stained beech. I've seen a couple of these that appear to have had some type of clear coat applied a long time ago and is now crazing. If your beech frame with walnut stain has worn areas that are lighter, neutral Restore-a-finish would not return the worn area to match the existing finish, but instead just darken the exposed beech.
Posting detailed photos of the area in question would be beneficial.

The Selig catalog referred to...
The Selig catalog referred to this finish as "Saddle". It is a tinted lacquer on beech, meant to mimic the appearance of walnut. You can clearly see the "shadow" on the chair frame where the cushions were, where they protected the finish from UV sunlight, which has faded the original brown color on the rest of the chair, turning it from brown to a greenish color. This is typical of how this finish shows its age, since the brown tinting stain used at the factory was subject to sun fading.
As others have already said, you would have to strip and sand the old finish from the chair. It is not an easy finish to restore, as beech often takes stain very unevenly, and even using a sprayed on tinted lacquer, you may have to use a pre-stain sealer on the wood to keep areas from looking blotchy.

here are some photos of the problem spot.
see below for photos of what happened when i applied the walnut finish.
i wonder if even the average restore professional would be able to manage a full restore on this, given the complexity of the process and my (impossible?) desire to restore to original form.
i need to remember that this is a sweet chair no matter how i slice it.

If you're looking for a pro...
If you're looking for a pro to do it, I'd recommend asking the candidate whether they've dealt with beech before. If they have, ask them to describe any special considerations. I think the keywords you're hoping they'll use are "grain filler" or "pore filler", as these are the generally-accepted methods to evenly stain beech. I can tell you I tried to stain my chair (not Selig, but Dux by Folke Ohlsson) several times before giving up. It's currently in storage and I'm seriously considering ebonizing it (and its mate). That's not a path I consider lightly; they really are that difficult to get a satisfactory finish out of.

I had a chair with this finish.
It was very greenish. Most unattractive.
I stripped the finish off completely and then ebonized it with permanent India ink followed with a paste wax finish. It was quite lovely, if I do say so myself. The India ink worked well on the variety of woods in the chair and was very easy to apply with just a 1" foam brush. I did one coat plus touchups here and there.

Wouldn't this chair also...
Wouldn't this chair also look pretty good sanded clean with a traditional danish soap finish. (I think a soap finish on a light wood, like beech, light oak, ash, maple, birch looks really natural).

danish beech
I am currently stripping the same selig z chair in beech. I had an illum wikkelso rocking chair that was also in danish beech that I sanded down and only finished with boiled linseed oil. It looks pretty nice as you get some reddish hue with the golden brown. I plan on doing the same thing with the z chair. You don't have to worry about uneven finishes and no worries about lacquer/varnish rubbing off. On a side note, I have many kofod larsen selig chairs in beech that I have stained using watco danish oil (medium walnut), you just need to do about 6 coats to get a nice even finish with a nice buildup of varnish to protect it.

Speaking of which, I have...
Speaking of which, I have refinished a Yugoslav pseudo Wegner rocker that was raw beech with a tung oil finish (Formby's) tinted with a blend of artists oil paints. Made it a teak like orange brown. And the oil tint was very even.
It is hard to say what to best do with a high value design like this executed in stained beech. I would be stumped.

Please keep us updated
Thanks for the ideas, all.
Oskar, would you mind sharing pictures of the results of your Z chair project? I like the simplicity of your approach, and imagine it should yield a beautiful look.
Of course, I'm in intimidated even of the idea of stripping this thing...

I should have it done within...
I should have it done within a week or two. Just have one more arm to go. Here are the pictures of the wikkelso rocking chair. It had previously been painted white.