When the headlights are in the AUTO position, I never have to turn them on or off. The daytime running lights are always on, when it gets dark enough outside the sensor is tripped and the headlights come on. When I park it at night and turn the car off, the headlights stay on. Once I am out of the car and push the lock button on the factory key remote from Lexus once, the doors will lock, but the headlights are still on. About one minute later the headlights turn off. If I push the lock button twice the doors will lock and the headlights turn off immediately. If I do not lock the doors I think, that the lights will turn off after the delay has expired? Not sure though, I always lock my doors.
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That's exactly the way mine work also, GS400