Something funny is going on in my '54 Customline. My dad called me the other day and told me that the right rear light was on... I checked, and all svitches were of, but if I turned the right indicator on (with ignition off) the light went out... Any ideas?
Unless I'm confused...which happens more and more frequently, it seems...if your car is still positive ground you might have a short somewhere in the rear turn signal wire. Keep in mind that the car body is "+" and the wires are "-" so the wire can become energized at any point along its length. The positive ground system is safer than a negative ground system because any short circuits are lower amperage and tend not to cause sparks, and thus fewer fires. It's a good thing, too, because the fabric wrap on the wiring of these cars is often in very sad shape. But, because the car is still positive ground, electrical problems will be more like yours and not the violent sparks of a negative ground short-to-ground. So, if checking the switch as was suggested earlier doesn't solve the problem, look along the length of the wire, looking for bare spots where the exposed wire can touch the metal body. Good luck!
Check for good grounds at the rear lights (both). Bad ground can cause back feeding to/from other circuits and cause strange things to happen. I use a volt/ohm meter to check between the light socket and the body and then do a good visual check for corrosion and paint.