Headlights draining battery at night

What causes the headlights (daytime running lights) on our '03 Corolla to turn on when the car is parked and ignition is off in the middle of the night? All light switches at the controls are turned off, and we cannot make the headlights turn off. This phenomenon has drained our battery three nights in a row (a new battery - Duralast - was purchased in El Paso after the first night). We are traveling across country from San Diego to Charlotte, and after we get a jump, the car and lights operate properly the rest of the day; nighttime temps have been in the 20’s.

I’m sure there’s some control module, under the dash maybe, that’s flaky. As a stop gap for the trip you could just unplug the bulbs after they cool at night.

I assume the DRL lights turn on when you turn the ignition on. If that is so then I would first check for a problem with the ignition switch.

For now, when you stop for the night, remove the Main Headlight 40A fuse. It should be under the hood, in the fuse/relay box. When you get to where you’re going, find a good automotive electrician, as these electrical circuits are complex. The right person will save you a lot of “experimental parts replacement”.