It's the solenoid. It's stuck or fried or both.
I cleared the tight shielding away from the solenoid plug. removed the plug to the single-wire terminal on the solenoid. Verified I had hot 12v on the big cable coming to it.
Checked my trusty old starter button for continuity and it works.
Attached the two alligator clips on the button to the 12v and the single-pole terminal on the solenoid. No click. removed the clips and tried it twice. Looks like I burnt the solenoid out trying to start it when the motor was stuck.
No fun. TIS says to remove the exhaust manifold on that side to service the starter. :-(
Meanwhile, VMWare on my laptop forgot where DIS is, I'm in contact with the guy who helped me set it up to figure that out. But I get to do another fun hardware job first.