351PCM - Weird Starter problem

Hello. I have a ski boat with a Ford engine (1994 351PCM).
It has a starting (starter) issue. Hopefully someone can offer some clues as to what's behind it. I'll list what I know so far:

- I have good power to the solenoid (12V).
- Turning key (ignition), I hear the solenoid click. no starter.
- I jump the connections at the solenoid, starter spins fine.
- I go back to the ignition, it turns over fine, as if no problem.
- I try the ignition again next time, solenoid only, again.
- I jump the solenoid again, starter still spins fine.
- Back the ignition, turns over fine.
- yet on next try, same deal, no starter....

I can repeat this over and over.
For some reason, if I spin the engine (socket on harmonic balancer) then the next ignition try usually gets a start. not always, sometimes takes a few tries. Once in a while, it does start fine... rarely. Mostly if it's been run recently. Not a flywheel issue, teeth are all good.

Something between the starter and solenoid?? Being a boat, moisture is around sometimes. But strange the repeatable sequence that gets it to go. No single component seems faulty, but together something is haywire.

Thanks for any clues!! Jim

From what you explained I would be inclined to replace the solenoid.