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Sounds like the starter solenoid is in a partway stuck position. The question is why...
Remove the start wire that comes from the ignition switch, that's plugged onto the solenoid.
Then check to see if there is power going through the solenoid by checking the back terminal, that leads to the starter. If you get ANY amount of power through here, replace the solenoid.
Then check the start wire from the ignition switch, that hooks up to the solenoid. With the switch in the off position, if the wire is hot, check wires and/or replace ignition switch.
If the starter engaged the flywheel for too long, the starter's gear could also be toasted, and needs to be replaced. Also you may need a new flywheel if it got damaged. Check the state of the teeth, when you have the starter removed.
That is the same thing that happened on my classic John Deere tractor. I would press on the starter pedal and it would do the same thing you're talking about. It would only stop if I disconnected the battery. The problem was the rod that starts the starter was grounding with the starter itself. Ohhh wait, thats not how truck starters work....is it. LOL!
Same thing happened to my van. Started it but the starter stayed engaged, cut the key off and it kept cranking. The starter solenoid up by the battery was worn [20 years worth] and the contacts "stuck" making it run on and on and on. Had to smack it with a handy piece of wood to get it to stop.
The solenoid is a cheap part [$10-$15] and easy to replace. Hopefully the episode didn't kill your starter. Mine died about two weeks later from cranking for a good minute solid... its guts were pretty toasty. The bearings were also a bit loose from spinning at ~1200 rpm for several seconds while the engine was running.
I have a new solenoid ill put on then check the starter. The only things I have done to the truck are installed a new clutch kit, new flywheel (koi had a deal on them) rear main. Also near the solenoid there was some corroded wires I replaced (orange and green wire spliced to a yellow wire) one is ignition the other is headlights.
I have been putting a lot of stress on the solenoid due to a bad carb and trying to get the truck running so hopefully my problem stops there.