I have run across this "many" times, even with cars and trucks. Nine times out of ten, if you hit the starter with a hammer, it will work. I know,, it sounds crude but will get you down the road.
What often times happens is one or two segments on the armature goes bad and when the starter motor coasts to a stop, just by bad luck, it will stop where the brushes contact a bad segment and the click you hear is the solenoid. A sharp hit with a hammer usually jars it enough to the next good segment. The odds are slim that the starter will coast to a stop in the exact same spot, but it does happen. I had to do this two times in the last year to my 87 Toy PU truck