Anyway, the head unit in my JK stopped turning off when I took the key out - so that was a fun battery-draining episode. I've been waiting for the weather to get nice to pull the head unit and put something else in there, so in the mean time I just pulled the fuse.
Of course the head unit is responsible for publishing outside temperature to the CAN. I don't care that the dashboard says --F instead of a temperature now, but on a cold start, the ECU doesn't know if the oil pressure is high because of a fault of just because the oil is cold. So if I get on the throttle even a little before the engine is warm, I get a CEL now. The joys of Jeep ownership.