1979 F150 sticking starter solenoid

[Snot Rod]

My starter solenoid sticks intermittently and has caused a lot of damage recently. I have replaced it twice, along with the starter and battery cables when they all got super hot and drained the battery.
I have also replaced the alternator and voltage regulator thinking I had an intermittent short holding the solenoid on. I have ohmed out the ignition swith for shorts and found none. This morning when it happened again I disconnected the battery to keep the starter from spinning but the solenoid was still on, so as soon as I touched the cable to the post it would kick on the starter. I disconnected the red wire from the "S" terminal and it was still on. Finally, I disconnected the black wire from the "I" terminal and I heard the solenoid deactivate. Does anyone know where this wire goes? Is it to the ignition module? I left the wire off and re-connected my battery then the truck started and ran fine, for now.
I'm new to the board and any help I can get will be greatly appreciated...

Paul