Q: If the starter has full-time 12v red power, and the casing is gounded, why doesn't it spin all the time? Does the solenoid make the starter power-up as well as kick out the cog?
Yes, exactly.
I believe your starter has two terminals. Both get +12V, but the BIG RED WIRE with the large terminal should be 12V straight from the battery + post (or else from the solenoid, but on the Bat side). When the fender solenoid engages, the small terminal 12V is sent to the starter. That pulls in a magnetic relay inside the starter that you can hear go CLACK. Out goes the gear to the flywheel and a set of contacts close, powering the motor.
The large red terminal has no power, so the starter doesn't turn.
Yes, exactly.
I believe your starter has two terminals. Both get +12V, but the BIG RED WIRE with the large terminal should be 12V straight from the battery + post (or else from the solenoid, but on the Bat side). When the fender solenoid engages, the small terminal 12V is sent to the starter. That pulls in a magnetic relay inside the starter that you can hear go CLACK. Out goes the gear to the flywheel and a set of contacts close, powering the motor.
The large red terminal has no power, so the starter doesn't turn.