I have a 92 f150. Sometimes after the engine has started the starter will stay engaged even after i have turned the switch back off.

 

The problem is more then likely the fender mounted starter solenoid. Not an expensive part,so you may want to replace it right away for peace of mind.Try to pay at least $15 or more for it. There are too many generic offerings out there on this part,so don't go cheap,it's the difference between $8 or $15 and a $200 starter and flywheel swap.Also pay attention to the location of the battery cable when replacing this part. Some manufacturers have a paper in/on the box to detail which post they want the battery cable to go to,very important on a Standard brand solenoid and possibly others to prevent sticking of the contact inside the solenoid.
Phillip