Cold showers are actually kind of nice when you're in the Keys since the "cold" water isn't terribly so having been piped down quite a distance. A cold shower in Chicago after you get back is a whole different creature.
Anyway, figured it was almost certainly a bad thermocouple, and since those are $5-10 I just snagged a new one (in the next size up - manufacturers use odd sizes, the replacements are all 18, 24, 30, etc. inches and you can just coil the extra) and spent some time trying to get the old one out.
And some more time.
Laying on my back, looking at the ceiling, with my left hand stuck through the little hole in the bottom of the water heater, operating by touch and not having much luck.
Finally ended up just pulling the old one out by its connector cable (it was a slide-in, some are screwed in and just pulling is probably a bad approach for those) on the basis that if that didn't work, I was going to have to either call a plumber or remove the entire pilot assembly anyways, so why not?
Since that worked I now have hot water, have replaced one, and feel resonably safe about doing the same up at my parents' place if they need it done.
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