Well, the new timing relay didn't fix it. I'm thinking there's some corrosion in a connector or something cutting down the voltage to the solenoid. Without a wiring and connector location diagram, I don't know where the involved connectors are. Recent shoulder surgery prevents me from crawling under and blindly poking around, so I did the bypass I talked about, Installed a push button connected to power and the pull in wire. It works great, turn the key on, bump the new button, the solenoid snaps in, and then start as normal. Not a true repair, but it works fine. Thanks everyone for all the info.