In my experience tail light problems have almost always been tied to a grounding problem. Bulb grounds through the socket, relying on the spring clips to make good contact on a bare metal edge of the mounting hole, which gets rusty and corroded over time caused me a lot of headaches. The wiring you show is the old woven insulation wire, so who knows what problems lurk in the depths of the '53 after 60 years. I'd double check every ground before chasing much else.