1974 Plymouth Duster Electrical problems when hot

There's a lot of different things that could be wrong and yet several possibilities might be really simple

MV8 already mentioned a couple How old is the battery? What is your "feel" for it's condition?

Do you have a factory service manual. If you send me a PM (conversation) I can help you with that for nothing more than some postage.

So Old battery? Battery fully charged? Battery defective? Dirty posts/ clamps? CLEAN then, don't just guess. Check the starter where the main cables bolt on are they tight? Battery main ground should go to ENGINE block.

Charging when operating? Do you still have an operating ammeter? It should be in mid point in normal operation after battery charges up normal. Turning on headlamps with engine stopped should move to left of center showing discharge. After starting engine, ammeter should register to right of center until battery comes up on full charge.

Other issues when hot is starter may be suffering from "heat soak." Normally a good healthy starter won't give trouble. A modern "mini" starter (like off a 90's 5.2 or 5.9 RAM or Dakota draws way less battery current than the big old original starters.