Tapping on the starter and making it work temporarily tells me you have bad starter brushes- - - -too short to make good contact with the armature consistently. Jiggling the battery cable and getting a circuit is another problem- - - -dirty connections. Remove both cables and give everything a thorough scrubbing with a wire brush both the battery posts and the inside of the cable clamps. Parts stores sell a special round brush that's made for cleaning battery connections, with male and female brushes built into the same tool.

Clean the cables and the battery posts, and rebuild the starter.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!