I recently fixed the driver's side h/light on my 1992 LT1. The problem was the delrin bushes in the motor/gearbox assy. Sounds like yours may be a simple d.c. supply problem, though. When I removed the whole light assembly to work on it on my bench, I first had to dis the electrical connections, which are on a grey plug/socket unit in the area forward of the wheel. Once that was off, I found the feed to the headlight was taped-up, covering it AND the feed to the lift-motor which had been spliced into the cable-form. I cut the motor wiring and (when the fault was fixed and I re-assembled the whole thing) re-made the motor connections with spade terminals. This approach also permitted me to 'run' the motor on a test-rig using a 12v.d.c. psu. What I am getting at, in a round-about way, is that if you identify and separate-out the d.c. wiring to the motor, you can connect 12v. to it and see if it runs. (Use a battery if you don't have a proper psu, but be ready to remove the voltage once the motor has run enough to prove it's OK). If the motor runs and the headlight doesn't lift, you need to get into the little gear-box. It isn't diifficult, but as mentioned above, it's a damn sight easier to work on it if the headlamp assy is off the car.
Good luck
Jack Cooper (in merrie Olde England)
1992 LT1