Another Saarinen tulip repair question  

seek out a chemist
it seems likely to me that any chemical that would break down the adhesive's structure could also do damage to the surface of the shell itself. but i'm no chemist...
if it were mine, i would be inclined to get in touch with the manufacturers of those types of construction adhesives [macco and pl, for starters]. i would think those folks should get you sniffing in the right direction.
here are some numbers:
* * *
Macco Adhesives
15885 West Sprague Road.
Strongsville, OH 44136
Phone: (800) 634-0015
Email: liquidnails@ici.com
* * *
PL Adhesives
Customer Service: 1-800-999-8920
Technical Service: 1-800-624-7767

Some glues
respond to heat. A heat gun (or hair dryer) directed at any visible glue will show you whether this adhesive can be softened with heat. I don't know what resins are used in the chair shell itself, so proceed with caution, of course. . .

seems like all the tulips ...
seems like all the tulips are dying at once ,after 50 years they are just wilting away .
The only advise I will give anyone is since lots of the Europeans do not appreciate it or care for it is .....
from experience they are very difficult to repair they require, to be re fiberglassed to fix the cracks,
glue is a poor substitute that looks like crap, but if you are in to the garage sale look that will be ok for you, . to dis engage from stand is tricky, you need a teeth less vice and then it has to be put back on right, . that is so you will not take the paint off and leave grooves,
use a professional or they will be trashed and ready for the dumpster and their final resting place, NO substitute for quality and they will tell you the price,

LRF,
Can you clarify how the...
LRF,
Can you clarify how the vice is to be used? Do you use it to grab onto the base and somehow pull the chair apart? Keep in mind that the base appears to be SOLIDLY glued onto the bottom of the seat.
Better yet, LRF, do you feel up to the job? 🙂
I have been able to hog out some of the adhesive between the base and the seat and I've tried putting in some Xylene in there. It seems to dissolve some of the adhesive, but it really needs to get all the way in there to do it's work... and that's where I'm stuck. Since the seat is recessed a bit, it's nearly impossible to get up in between the seat and the pedestal to with a pallet knife or any thing like that. It's been very frustrating.
The jerk that sold me the chair said it was in excellent "original" condition. Now his eBay ID is NARU'd and doesn't answer my hails...gee I wonder why?

Fungus Mungus
i know that is tuff stuff I would use the heat to dissolve some of that crap/. that is why i thought a vise grip with no teeth would do good,

Thx, will give the heatgun a ...
Thx, will give the heatgun a try.

heat
try it on an invisible spot as the heat needed to melt the glue may also melt the fibreglass.