Tested the rudder position sensor again tonight and it checked out fine.

Just on a hunch, I went back to check the drive motor wires again: I had checked these crimp connectors before (even test-pulled the wires and separated the crimp connections and rejoined them) and also tested the motor with raw battery 12v power through these connections, successfully. But tonight after the RPS tested good I decided to replace the wire itself... I started by putting NEW crimp connectors on the motor inputs, then (just for a test before using the new wire) I cut the old crimp connectors off the old supply wire and replaced them with new crimps. I put them together and tested the AP and VOILA!!! It worked with the old wire, as it should.

So I have to acknowledge SG who wins the prize in this thread. He guessed it. It seems that the controller varies the speed and it's output is generally not at a full 12v, so at the lower voltage the motor couldn't pull the amps needed to start under load, through the marginal connection. When I tested it through the same marginal connection at 12v the motor started and ran. So all I needed to do was replace two pairs of crimp connectors.

Thank you everyone, for your thoughtful input. Who'd have guessed it would be a 50-cent fix?