Since the ballast is bypassed in start and he's only getting spark in run I seriously doubt it's the ballast resistor.

Since you get a spark at all I doubt it is the coil.

Since the ignition switch is what bypasses the ballast I suspect that or the wiring/connectors.

They say there are no such thing as a stupid question.
They say there is always the exception that proves the rule.
Don't be the exception.