There’s lots of people who’ve had this error, and lots of information on the net about how to fix it. The consensus appears to be that, more often than not, it’s just a bad contact and NOT a failed solenoid. (Edit: It’s not the contact, it’s the solenoid – see below)
This is extremely handy, because replacing the solenoid is a pain in the arse!
However, those solenoids are JUST reachable if you don’t mind a few scratches from bits and pieces, and you can actually remove and re-seat the connector without needing to pull the top of the engine off.
After pulling it out (and if you do this, NEVER put any stress on the wire, ONLY pull on the plug), spraying some contact cleaner in, and putting it back, this miraculous thing happened!
I did have to clear the error first, obviously, and I then took it for a good bit of a brap around Gladstone, getting it up to temperature, running it up to the redline and generally exercising it. It didn’t come back on!
People have mentioned that it’s used when the engine is COLD, but the engine was obviously cold when I was messing around with it, so I’m feeling hopeful. It is possible that the solenoid is just getting old and is unreliable, in which case it’ll come back on and I’ll have to bite the bullet and replace it which does entail pulling the top of the engine off.
Edit, the next day: Well, my hopes and dreams were crushed. The CEL light came back on, so it looks like I will need to replace the solenoid. I might as well replace all three, as they’re $13 from China (and $140 from Mazda!).