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my 2000 c5 headlamps pop up and turn on when i turn off the ignition. i stroke the headlight stalk from off to on to off again and they go down and turn off. (the twilight sentinel system is on the off position) Number two .......sometimes ....... minutes later i notice that the headlamps have popped up and turned on again and i have to repeat the process to shut them off......kinda spooky or just an electrical short ????
Theres a TSB out for the drivers side headlight popping up after shutdown. If its both headlights thats not the problem
If its both lamps the prime candidates are the headlight switch on the stalk or the hazard switch going bad. both are common failures.
Try turning twilight sentinel on and see if the lights work normaly. If so its probably the headlight switch.
The easy fix is to lubricate the headlight switch with some electronics cleaner and see if it improves. Its been known to fix the problem permanently. If that doesn't work I'd try the headlight switch replacement first as its a bit easier. Both fixes are documented so try a search.