I think that the headlight motors on the 88's and up use a current sensing module to sense when the headlight motor has opened or closed the door. When the motor stalls, the amps rise up and the module stops the juice flow. The mdule is way up front on the drivers side down and near the radiator and the canister.
Each motor has three or four (i think) plastic shear pins that connect the motor drive to the output shaft taht turns the tubs. I think your driver's side motor has sheared the pins. When this happens, the motor shaft slips and there is not enpough current rise to trigger the module. The module has an internal timer that stops the motor in a few seconds if the current fails to respond. I think that is a really nice design. Midwest, Ecklers, etc. sell a kit to buy the shear pins. It's just a few bucks and is pretty easy to do. I have not had to deal with yet myself but I have read about this problem many times. What ever you do, don't use metal shear pins because you can badly damage the motors if something jams the works and the module does not break the power off.
The older cars used a different headlight motor with relays and end switches to sense when the tub reached the end of travel. These older motors have a plastic nylon gear that has teeth to shear off if the motor does not stop.
