Do the wiggle test also just use a good pair of insulated needlenose pliers if you use your fingers you can get bit pretty good just wiggle the wires
Intermittent faults are normally wiring related. Before taking it to a mechanic go through and clean all connectors with electrical cleaner and put back
While the old original Bendix Drive starter motor is heavy and looks tougher than nails...... the technology is completely outdated by now.
If you shorted the blue coil wires to battery pos you need new coils even for a split second. To kill the motor you short the two blue wires together
That's a good start.
If operating in saltwater or mud/sand conditions, I suggest getting the entire water pump. Sputtering throttle could