Maybe depends on the particular spot the starter motor stopped on after the start? Dirty rotor and worn brushes equals sometimes good connection, sometimes not so good?

MH has an onan generator. Tried to start it and nothing. Someone told me to remove a plate and sand what was exposed, being the commutator. Sounds like the little door plate is for that purpose? I think I used scotch-brite. Lit right up. Had the engine bib off the MH, tried to start the engine this time. Replaced the starter relay and no joy. For some reason, out of the corner of my eye, I saw a spark. Took that steel braided cable off, filed the rust at the eyelet ends and frame... lit right off.

With two personal experiences, one, your generic... hold on I just thought... have an electric leaf blower. It was just running. Pull it down to check the switch.. good. Then I think commutator. Scotched it up... fires right back up. So as I was saying, a coating on the copper, or rust at the engine ground cable, of the 3 mentioned, none of them started. Yours keeps starting. It has to not start at all... or you're wasting time and parts.

Bop cured his with a relay. You can take a test light, probe the cable right at the motor's stud. This way you are about to remove the motor... IF ... you push the start button, no test light lights up first click, but second try, you see the test light at the motor's stud light up and so does the engine = Relay, not dirty commutator.