(quoted from post at 08:20:29 07/28/20)
The system I am most "familiar with" (Ford) does, in most cases use the solenoid to feed 12 volts to the coil during "start".
However, not all systems work that way.
I went out and looked at my D-17 Ser II and there is only one terminal on the solenoid other than the heavy duty ones.
When I looked at the diagram of the ignition switch in the parts manual, it appears it has both S and I terminals which leads me to believe that, in this case, the ign sw is the controller of voltage to the coil in both start and run modes.
It appears that some D-17s use a separate push button starter switch. Not sure how the process works there.
I have no idea whether or not the ign sw is causing the coil to overheat; I just threw it out there as a potential reason.
"ignition switch has both S and I terminals"
"S" sends power to starter solenoid during cranking, "I" powers the ignition system during cranking AND normal operation, no provision for a starting bypass there, another terminal sending poser to the coil side of the ballast resistor would be needed.
What you may be overlooking is this... there are two types of ignition ballast resistors, a basic type that has a fairly constant resistance as it warms up, typically used with a "starting bypass" circuit", and the "PTC" (positive temperature coefficient) type. The "PTC" ballast resistors are commonly used in ignition circuits WITHOUT a "starting bypass". When the ignition is first switched "ON" the resistor has a low resistance for good spark during cranking, then it's resistance increases as it heats from current flowing through it to a safe operating level.