After reconnecting, I tested the starter. It slowly engaged and just barely turned over. Odd. Batteries haven't been charged since November, but I had just checked the voltage (I always do in the spring), and they had lost no more than 5% charge.
Turned the key again, and...nothing. No click. Dead. Must be my wiring so I checked voltage along the route. Everything checked. Disconnected the power from ignition key switch to the solenoid, and checked voltage. All good, same everywhere. Reconnected that line to the starter, turned the key to energize the solenoid while checking the voltage on the key switch, and voltage dropped like a rock.
Further, I couldn't get the starter to run as I bypassed the solenoid. This is a dodgy move though, as sparks fly when an arc makes the high amp connection through a screw driver - jammed into the lugs.
That would be weird, wouldn't it? Starter and solenoid, suddenly both die?
Curiosity got the better of me and after pulling the starter and taking it home, I took the solenoid off. I could tell that it was cooked. It had that odd smell of a burned electrical stuff. No matter how well I grounded the solenoid in a vise, power to energize the coil did nothing. Dead.
Put the starter in the vise with a negative cable terminal clamped in the jaws, touched the + cable to starter lead, ZAP, and it ran.
I'm waiting to catch the starter guy RC mentioned, on the phone. He's one of those dwindling businesses that has no online presence. There are a few still around. Glad this happened, now.