I ran into an odd electrical problem like this a few years ago while making a Model A streetable that had been an amateur messtoration, complete with the expected shortcomings. A local special interest car place called and asked me to make the dual tail and brake lights work. No matter what their in-house mechanic did, he couldn't get them to work, even after replacing the entire lighting harness and changing bulbs numerous times. I, too, ran into a brick wall for a while until I happened to notice while on my back for the umpteenth time that the underside of the rear fender above me had an odd surface. Not shiny, but kind of crinkly. Sure enough! The beautifully painted rear fender on top was made of FIBERGLASS! No WONDER the rear lights and brake lights wouldn't work! Fiberglass is non-conductive, so there was no grounding ability. I ran a wire from a tailight mounting stand bolt on each side to a good ground spot on the chassis and viola! Let there be light! Another head scratcher solved.
Next time you encounter such a problem with someone else's Model A, ensure that the rear fenders are Henry's STEEL and that the taillight stand has a good ground against the rear fender surface.
Marshall