So I got two free timers from Orbit after I called them.
I hooked up one of the new ones, and it still doesn’t work. There is supposed to be 24VAC at the terminal when it’s running, and the voltage is zero. Just to be sure, I checked the resistance on a couple of the solenoids, and it’s about 70 ohms (the reactance is no doubt quite a bit higher on AC). But clearly, if there is no voltage at the terminal, the solenoid isn’t going to open. I went to the Orbit site for troubleshooting, and it says that if there is no voltage at the terminals, the timer has to be replaced…
At this point, I’m wondering if the system is haunted.
[Update Saturday evening]
People commenting, go back and read the original thread. I’m not clueless. I’m pretty sure that if there was a short to ground, I’d see it when I measured the resistance on the solenoids.
OK, it finally occurred to me to check that it was getting 24VAC input. It wasn’t. The upstream GFCI had tripped and the transformer wasn’t outputting…
One of the ones I took off had an indicator saying “No AC,” but I swear I didn’t see that when I was working on it. I now have five of them, four of them (AFAIK) functional. I’ll return at least three to Home Depot (since that’s how many I bought there).
[Update a while later]
And yes, I was a dumbass.