I’m having a bunch of these restored by a retired gentleman that does this in his spare time. He and I were just discussing using compass fluid . Marine and aviation sources will supply this. Also this compass although a terrific looking design is one that is very poorly engineered. They’re notorious leakers. And most of the critical parts like the bowl, the backing plate and dial are all subject to cracking. He repairs them with JB weld. However the problem sometimes comes back. Also he fills them inside an another container of fluid and is thus able to fill the bowls all the way to the top without much air inside.
also don’t know if it matters or not , but just as s as n interest in discussing I believe these beaconlite models were made a little later than the 1936 timeframe of your car. I could be wrong but the earlier ones - streamline were patent dates of 1934-1936. They were famously used in ww2 tanks jeeps etc. That body design also came in a lighted model, probably called beaconlite as well. I’ve seen 1939 ads showing them. The earliest I believe the elongated beacon lite like you have, would be around 1948? I’m just going by info I’ve gathered so far. Then there’s the all plastic egg shaped ones that work really well but are a late 1957 patent date. Good luck!