When you reconnected the battery, the headlight control module
drives the headlight buckets to the closed position. You probably
never noticed the motors continuing to run because the hood was
always closed. I'm assuming it was open when you noticed
the motors running?
You need to install 3 Delrin bushings in each motor.
They act as a clutch for the motor. From the factory from what
I've seen a gel was used for the clutch. The gel eventually
dries out and turns into a powder. Some people say bushings were used. Anyways the bushings are available from Corvette part places or any auto part store in the Help isle. The same bushings are used to repair older Ford power window motors.
Buy Dorman - Help Window Regulator Gear Plugs - Ford 2006-65 74410 at Advance Auto Parts
Here's a video where the person is replacing the driven gear but
he shows the bushing installation.
On one of the motors to reinstall the driven gear because of the
way the gear teeth are cut you need to loosen the three bolts holding the motor housing halfs together.
Don't completely remove the bolts because if the housing
seperates you will have to reset the brushes. When you
pull the housing apart that will give you enough clearance
to push the driven gear back into position. Some people file
the gear teeth down.
How to change the headlight motor gear in a C4 Corvette - YouTube