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I have an 01 Z06 and when I turn off the headlights they both go down alright but the drivers side motor will continue to run for about 10-15 seconds after they have both gone down.
Do a search on this topic - there are many posts about this type of problem.
If you hear the headlight motor continuing to run after the door closes, the plastic gear in the motor is likely stripped - an aftermarket brass gear can be installed to fix it.
If the door continues to reopen after it closes, then the plastic stop that the motor arm contacts is broken or missing and needs to be replaced.
I have an 01 Z06 and when I turn off the headlights they both go down alright but the drivers side motor will continue to run for about 10-15 seconds after they have both gone down.