Karl, I agree with Ross the finish is probably lacquer, but in that time frame it could be many other things, I would do a solvent test to be sure. Below is something I wrote for a refinishing class that may help.
I must admit that I strip a lot of furniture, in fact so much that I buy stripper in 55 gallon drums. I have tried many methods and products, including the green versions. I can honestly say that for me nothing has worked as well or as fast as heated, thin, wax release, methylene chloride stripper. I currently use a flow over system where the hot stripper is pumped through a scrub brush and recycled and pumped again. With this system I can strip about 12 chairs an hour, or a dresser in under 20 minutes if not painted, if painted it takes a little longer. Before I used the flow over system I used heated, thin, wax release methylene chloride, scrubbed with saw dust and shavings. These are the steps I used in this system.
1. Spread about 1 inch of shavings and saw dust on a clean concrete floor in an area larger than the item being stripped. This will contain the mess of the stripper.
2. Apply the stripper with a large mop type brush, the goal is to cover the item as fast as possible, you want to keep the item wet by applying over and over until the finish is totally dissolved. You can tell when the finish is dissolved because the application brush will move the finish around easily. The key here is to let the stripper do the work, and not waste time trying to scrape off the finish and stripper, if you scrap off the stripper before the finish is dissolved you just have to reapply it any way, why not just apply again without scraping. Pay attention to the nooks and crannies and keep going until the finish is dissolved in these areas.
3. Once the finish is totally dissolved begin to scrub the piece with hands full of shavings and saw dust. Use the shaving like it was steel wool, it will get into all the nook and crannies, it will soak up and remove all of the old finish if you let the stripper do it?s work, it will remove most pigment stain but not dye. Dye would need to be bleached.
4. At this point you neutralize the stripper, what you use depends on the stripper you used. If needed you can dry with more shavings.
5. Sweep up the shavings, if you used enough there will be no mess just sweep and your done.
Four things to note.
1. Some people will recommend using gelled stripper, in my experience the gelling agent dilutes the stripper and makes it weaker and you use much more to get the finish dissolved. The thin wax release stripper when applied releases a thin layer of wax that rises to the surface and helps keep the stripper from evaporating without weakening the stripper.
2. If you don?t have shavings you can buy them as pet bedding at pet stores.
3. Methylene chloride fumes are heavier than air, you need to ventilate at ground level.
4. There is no way to describe the difference between cold and hot stripper if you have not tried it. However you must do it safely. The biggest disadvantage is it makes the stripper evaporate quicker.
I am not recommending any one use these methods, I don?t know if these methods are less safe than any other method. This is just what I do you must make your own decisions.