That is unusual. I would definitely disconnect the 304 WH 10 white wire at the starter solenoid in that case, and run a wire to the cab to a temporary red LED bulb where you can't miss it, then test by trying to start it to make sure the light works. I would not risk damaging the starter by leaving that hooked up while running, and you won't know it's fixed without running it. You still have to be extremely careful for the noise of the starter if there is some way it could come on by itself, even with that wire disconnected.
The problem coming after 4 hours makes everything more complicated. I mentioned all the extra wires in that start circuit, and don't believe they are the issue, I have never seen a module fail and backfeed like that, but it is remotely possible. I'd suspect that would be the result of obvious rodent damage (chewing the wiring harness or urine) or saltwater which will act the same as mouse urine. Once you have the red LED light set up, and it lights up indicating the problem, then you can take your time diagnosing the problem, wiggling the harness, checking voltage etc.