[JM 35 Sedan]

I would check the coil, resistor on firwall behind dash, and condensor as Terry mentioned. These components could all work fine at ambient temperatures, but produce the problem you discribe when heated to engine operating temperatures.
Buying new reproduction replacement parts, with some or most coming from offshore sources, may be no better than what you have now. This could also be true for NOS replacement parts because of degradation of 80+ year old insulating materials.