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71 F-100 i just got. Had a problem getting the radio to work. It was wired to the starter side of the solenoid switch so i swapped it to the battery side of the switch and radio started working. Now, however, when i start the truck, the engine keeps running when i shut the key off and will continue to run until i disconnect the positive battery cable. One of the times the starter even continued to spin after the engine fired. I disconnected the radio wire completely and the problem persists. It already has a new ignition switch and the accessories all turn on and off properly so i dont think thats the problem, and none of this started happening until i started fumbling with the wiring on the solenoid switch
Additional to what I posted to your other thread of the same problem. There may be one or two harness pieces that connect to the starter side. These are used to supply 12v when cranking. Sounds like you may have that harness piece attached to the battery side. Hopefully you marked everything before you started swapping things around.
There should have been one wire (brown on mine I think) that went to the little side post of the solenoid furthest toward the firewall (usually marked with an I for ignition.) That needs to stay right there. If this got moved to the battery post then the ignition will always be hot and you won't be able to kill the motor.
Get the radio completely off the solenoid. The wiring is obviously badly honked. You have some strange feedback path.
You have two large posts on the solenoid: The one to the front is the main supply to the vehicle directly from the battery. Anything connected there- like your radio- will remain on until the battery goes dead or you disconnect it. The big lug to the rear is the starter. It only has volts when you are cranking. Nothing else should be there except the starter cable.
There are two little lugs: S and I. S only has volts when you want cranking and pulls the solenoid in. I feeds volts to the coil, bypassing a dropping resistor when the starter is drawing heavy current.
Get the radio off the solenoid and find a place to bite into ACC.
You should have no appliances on S or I or the big starter lug to the rear.
Also, while you have the solenoid off, scuff up the mount point to get a good ground and tighten mount bolts well.
I hope this helps you.
Semper Fi