if it starts jumping the relay even when hot, then it isn't an ignition component.

I would be checking the key switch or bulkhead, or even the wire that supplies power on start vs run.

since you can start it jumping the relay, the run power wire is good. but turning the key the start power to the coil, which bypasses the ballast resister has some heat issue. you will have to trace it back till you find the dead spot.