I had similar problems on my '39 sedan. I quite methodically disconnected and cleaned every connection in the circuits for both sides. Connections under the kidney cover were soldered. I also removed the sockets and bulbs to clean and reinstall. Don't forget about the switch at the bottom of the steering column. What a crappy idea to put it there. It gets caked with oil, grease and dirt. I opened mine up and could not believe the mess inside.
After all that, I finished by gently polishing the reflectors. A lot of work, but worth it in the end. Good luck, Tom.