Here is a video, from under the hood, recording when I tried to start it up this afternoon.
https://youtu.be/CmFh5H_Cgug
You will have to forward to 1:49 to hear the start up*. I cleaned up the solenoid, and as noted above the mechanical parts appeared to be functioning. I could push-pull the bendix lever, and reconnected the solenoid throw arm.

* As I wrote in my first post, the car was starting and running just fine. Except for the fact that it has always taken an insane amount of time to glow. The glow light stays on for 90 second easy when cold (like today). THE ONLY THING I had changed before my starting issues were the glow plug wires.
Longer story: The PO had (to my surprise) replaced the loop GPs, but kept the old 'bed spring' wires on. He had also substituted the relay fuse with a plain piece of copper wire . I put in an 80-Amp relay fuse (though I think it should be 50 AMP), and attempted to replace the wire with some 12 awg insulated copper I had around (didnt work or help). In the interim I broke one of the 'bed springs', and now have only 2 bed springs, connecting 3 glow plugs. It should be enough to start the car? Given all this I am wondering if I am some problem other than the starter.

If its clear I am trying to avoid pulling the starter, that is true. If I should just pull the starter, let me know. If I should solve the GP issues first, let me know.