It's been working only intermittently (and seemingly randomly) for a couple years now. I figured it was a bad ground in the latch mechanism, but I just took it all apart and cleaning it up (rust), and still no-go. I can hear the relay clicking in the dash, but the piston that releases the latch doesn't move. Not sure what to fiddle with next. Any ideas?

I would check the voltage at the solenoid and see if it's 12V+ every time you push the button. If it is I would replace the solenoid. If not then you have an intermittent wire somewhere between the relay and the solenoid.

See my Cave, Trunk Release
just poorly adjusted or dirty latch parts can cause power latch problems.
any switch(es) or relay can cause problems too.

need a simple test light to find what's wrong.

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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurassic Park)

The Ogre's Fiero Cave

The solenoid grounds through the lid latch. If it fails to operate, have an assistant reach under the lid lip and pull up on the lid. This will force the latch against the striker. Try the switch again and see if the solenoid works. If it does, tighten the striker to hold the lid down more.