With the starter on the bench I cleaned the terminals and set up a test.  Anyone who has worked on a GM car for about the last 70 years has probably seen a Delco starter.  Battery voltage goes to the big terminal.  When 12V is applied to the “S” terminal the solenoid engages and the motor runs.

So I got out my trusty 12V power supply (sometimes called a battery charger) and set up a test.

12V on the big terminal, ground on the frame, and a jumper wire on the “S” terminal.  When I touched the jumper to power this happened:

So the starter is good.  I cleaned up the hardware and put it back in.

I was still kind of hoping the solenoid had been stuck and it would work now.  But no joy.  So I pulled the spark plugs and ran a lead from the “S” terminal to the battery.  The engine cranked strong and fast.  So we have a wiring problem.  Dammit.