Depends on the place, most that I've ever dealt with were spliced into the harness. You got off lucky if they went the extra mile and used the less intrusive option. Those aren't as common.

If these things connect to the OBD port, aren't they basically trivial to find and uninstall yourself?

They're normally wired in somewhere behind the glovebox or steering column, and can be pretty hard to find.

I had one on a car I bought, and it kept draining the car battery whenever I left it more than a few days. I wasted many hours buying new batteries, testing alternators, and tracking down leakage currents before finding it consuming nearly a watt continuously.

Did you mean 1 Watt or actually 1 Amp? 1 Watt would be rather modest and shouldn't drain you battery within a week, 1 Amp certainly is another story.

1 watt. So about 0.1 amps. But the car had a 30 amp-hour battery, so after 10 days the battery is fully drained. And lead acid batteries don't like being fully drained more than once or twice, so after a month or two, you have to buy a new battery. And the process repeats...

This happens even if you drive the car every day. Since a full charge of a lead acid battery is 12+ hours, if you only drive the car half an hour per day, then each day you are discharging more than you charge.

Do they split the OBD signal behind the glovebox or the steering column? If so, then I imagine they're much harder to find. But if they do it on the actual OBD2 port, then I imagine they would be rather easy to spot?

They only need a power source to stay powered to give up their location. Most of them don't splice in nicely using the OBD ports.