That does sound like a bad ground. Easy to say from here, I know
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My father spent more than 30yrs with a similar problem on his old Jeep FC. After years of going under the truck with a screwdriver to jump the connections on the solenoid, he ended up installing a jumper wire to a switch in the dash for the days it was being a punk. He never did find the source...
I'm not sure why I went off on that anecdote...
lol. This problem is distinctly ringing a bell in the back of my mind but I can't get it into focus. I'll chime back in if I remember...
I'm sure you'll find the source one way or another, and make sure you let us all know what was the cause.
Good Luck!