these fireplaces... I know it is a waste, but I just pay for it throughout the spring and summer, so that I know it will light when I need it.

As to your question, I had one that the pilot light remain lit, but the auto igniting mechanism wouldn't work--even after I cleaned the venting areas well... Finally, out of frustration, I pounded (gently) on the glass in front of the lighting elements and it started working against. Not sure what that means, but it worked all last season with the intermittent tapping. I'm now in a new house with identical fireplace, but it is (fortunately) working well thus far without issues.

Good luck on your question.

and I also live in humidity/heat hell, so they aren't necessary but about 3 months out of the year. It got down to 25 last night, but that is kind of an oddity.

In any case, I don't think it is strictly the pilot at this point. It has been difficult to light in the past, but all signs (hard to light, staying on for about a minute and a half after lighting the pilot and switching it on with the remote) point to a bad thermistor that needs to be replaced.

I'll keep you updated on my progress, if you wish. They are awfully nice when it gets cold!

... similar to the flame rod in a gas furnace?

Can you clean off the carbon residue with sand paper?

First I'd check for corroded leads. When you're in that low a voltage range, it doesn't take much to futz up the works. Hopefully that's the problem, since it takes about two seconds and a knife or fingernail file to fix.

Set your MM to millivolts. With the pilot light on and switch off, the thermopile should be generating at least >250-350 millivolts, if it isn't, it's probably bad. When you flip the switch to turn the burners on, it should drop by about half. If it drops to zero or close to zero, it's got a short. If it doesn't drop at all, the problem might be in your switch.

With it set to ohms, stick the leads on either side of the thermistor, then turn on your pilot light. You should either see the resistance start to increase or decrease, depending on what kind it is. If it doesn't, it's probably bad. If it reads infinity, it's definitely bad.

I'm used to dealing with them from ovens and dryers and the like, not heaters, so take all that with a grain of salt.

Buy another thermopile or thermocouple, which ever one your fireplace uses, and swap it out.