I fiddle with our wood parts some, and other furniture projects...I agree that its bullet-proof, and my guess is an early catylized lacquer. The Europeans in the furniture industry were the first to start trying more alcohol and water resistant finishes in the late 60's and 70's (cat lacquer, and later, polyester flat line finishing, and polyuethane). I, too, have tried everything to strip, and finally resorted to abrasives. And even that takes alot of time, and sorta stinks. On some dashes that have top coat that has cracked and lifted, you can slide a thin pc of metal (an erasing shield, i.e.) or an xacto blade under and chip and pry (wear some glasses; small, sharp, shards flying at your face..), but often the "skin" pulls the first layer of veneer, or you get gouges in it. So, the patient use of abrasives is what I am using....usually assuming that the top layer will have to be replaced from slight sand-thoughs, etc, anyway.
On the other hand, I'm pretty sure they still used hide glue at that time, which is...de-lamination drum roll please...water soluble. Which is why our wood de-lams at the ends/corners...or in desert cars, the hide glue cooks and turns back into crystaline dust...its a harsh environment for wood in a cold, hot, wet, arid greenhouse...Sorry so wordy..
I agree with Gary, they should have dipped the whole car in the wood finish vat...