Starter stays engaged once in a while on my f-250 7.3 liter diese

Starter selonoid is sticking open.

I think you nailed it with the amount of time you glow plug light. It should stay on until you engage or it should be timed to stay on longer.

CALLED A DRAGGING STARTER...BEARING IS WORN OUT.

inhibit relay

Sounds like the starter solonoide is hanging up.
This condition can be remedied by replacing the starter soloniode on the starter motor.

DO NOT drive the truck with the starter enguaged... you will find electrical problems popping up if you do....

If you mean when you release the ignition key the starter stays engaged the electrical ignition switch will need to be replaced

It sounds like the small tickler wires may be reversed to the Solenoid.

If no success, call Itasca and ask if there were any changes for this Solenoid. There are several types of Solenoid with the grounding being the major internal difference. Most likely your wires are switched.

2 problems, first you have bad starter or starter relay for starter staying engaged, keep alt plugged in has nothing to do with starter staying engauged, to test starter relay, jump at relay bat + post with red/bk wire on solonoid, if cranks over without staying engaged, then not relay or starter but rather in your ign switch, ford had bad problems with ign switch some years ago doing that

The starter relay on the fender is the most common cause of this condition. ,It is on passenger side feder in the engine compartment, it is round and the positive cable of the battery goes to it,