Sometimes the spade(Flag) terminal on the solenoid can get a little corrosion on it and starter won't turn with key. When you pulled the connector off and reconnected it, you cleaned the terminal and the starter worked again.
The salt air on Prudence Island can do that. I live close to ocean in Westport and I have to connect and disconnect the start terminal on my Kubota every year or so. It probably has a similar brand of starter. Never had to do anything more, but if you were fussy, you could get some electric contact cleaner and spray the terminal connector and the spade.