Could be a faulty starter relay, could be a fault in the wiring, or it could be a faulty starter motor assembly (specifically, the starter solenoid, which is physically attached to the starter motor body).
I would recommend that you do what I suggested to another F150 owner in
this post - he had the same problem. What you would be doing is disabling the regular starter circuit and adding a manual starting wire.
That will quickly tell you if the fault is in the starter assembly or elsewhere. If the fault is in the starter then you have no option but to have it repaired or replaced, but if the fault is elsewhere then having the manual starting wire will enable you to keep the truck in use, and fix the fault later when you have some free time.
If you find you need to do some electrical fault-finding then all the information in post #6 on
this thread will be applicable to your vehicle, with the possible exception that the thin wire which connects to the small terminal on the starter motor assembly might be a different colour.