Sounds like a "sticking" magnetic starter relay . You can test the magnetic start relay and see if this is true or not. Disconnect the wires from the magnetic start # "A" and "B". These are the wires that energize the starter solenoid. Wire #214 connects directly to the starter solonoid, so disconnect it. Now connect your OHM METER to thhe tgwo contacts on the magnetic starter relay you previously disconnected, that is, contacts "A', and "B".
In this way you will be able to see if the magnetic starter relay contacts are sticking. Have your assistant push the start button, the ohm meter will show continuity. Release the start button, the ohm meter will show no continuity. Do this over and over again. and the ohm meter will show you if the relay is closing its contacts when you push the button, or not.
The second test will be the starter soloniod. if its "sticking" first, reconnect the wires to the relay , A & B. Then disconnect the wire 214 from the starter solenoid at the solenoid terminal # 1. Now make a " jumper" wire. Connect one end of the jumper wire from MAGNETIC STARTER RELAY , terminal "A". ( alligator clip type jumpers are a good choice here ) Hold the other end of your jumpoer in the ready...Tell your assistant to push the start button, and then momentarily touch your jumper to starter solonoid terninal #1 The solonoid should then energize the starter ( the engine may start, so dont be alarmed. Quickly remove your jumper form the starter solonoid. The starter motor should stop cranking. Do this over and over again and observe if the starter starts itself without your jumpering the solonoid. ) Keep us all posted ...