The gears aren't the problem, it is the Delrin bushings in the gears - they
turn to powder - you can get replacement kits for about $5.00 a side from
Eckler's but they are very labor intensive and require removal of the
headlamp assemblies.

Check to be sure the wiring harness is not interfering with the headlamp
bucket turning.  I was primed to swap out gears, motors, whatever, and found
that the cable tie that routes the harness had failed and the cable was
snagging the bucket.

If that is not the case, the nylon gears in the motor are designed to fail
and protect the motor.  It is either age (nylon deteriorates) or the bucket
was jammed and the motor overcame it (see above) or something.  Several of
the Corvette accessory stores sell replacement nylon gears.  They also sell
bronze gears that are more durable.  Here's a tip - the bronze gears are
stronger than the motor torque.  The motor costs a LOT more than the gears.
If you do the swap yourself (and you can but it will eat up a day for you),
swapping out the gears is probably the better route.  Unless you plan to
keep the car another 13 years, the nylon gears are probably the better
choice since you have 13 year old headlight bucket motors.