Bad grounds are the source of many electrical problems. If your '32 is glass it complicates the grounding issue even more, as you won't have the metal body to act as some of your ground circuit.

I would start right at the battery. Your ground probably goes to your engine block? If so, you also need something like a braided ground strap going from the engine or transmission to the frame. Then you need some kind of a central ground block under the dash (or somewhere) where all of your accessories electrically ground back to. This central connection has to be connected back to the battery negative post for the best connection.

The big clue here is when you say your power windows will also slow down. Your circuits are searching for a good ground. Make sure every connection is clean and bright and goes to a bare spot to ground to. Painted surfaces are not a good ground connection.

Don