Does the rear unit work on vacuum or electronic for actuation?
If it's electronic like the 1994+ rear HVAC systems, then this controls the rear vents.
You will need to unplug the connector and unscrew the three screws that mount it on.
If this is the part that moves the vent doors, then you will need to take it to Advance Auto. Just make sure you order the correct one. There are about 32 different types of this actuator.
As for the motor being straight wired in, if it's working, added an in-line fuse. Walmart sells the Bussman for a few dollars in the automotive section. If the motor is not working, the brushes are fried in the motor and you will need to replace it.