Wow...that's a new one. About the only thing that could cause this I'd think is some sort of short that when the backup lights come on (only when you're in reverse) or when the shifter itself is in this position, this somehow causes or fixes some sort of a short. You don't mention whether this is a column shift or console shift car, but I'll bet it's a column shifter? Assuming it's a column shifter, I'd probably be trying to get into the dash behind the speedometer and see if there's some wire that got rubbed raw from the sliding up and down action of the column shifter. If it's a console shifter, I really am not sure what it could be, but I'd get inside that console and see if there's something wrong with the wires.
Blown fuse? Bad blower motor? Bad blower motor resistor? Bad blower motor switch?
Could be, a blown fuse, a bad blower motor, a burned out blower motor speed resistor, a bad blower motor switch,
Defective blower motor or blower motor resistor pack.
No, that would have no bearing on the blower motor. Check the fuse, blower motor resistro pack, and the blower motor itself.
If you are referring to the blower motor squealing, then I would suspect the blower motor bearings have failed.
I would suspect the blower motor speed resistor is bad.
I would suspect the blower motor speed resister is shot.
blower motor bad or no power to it chech fuses blower switch blower motor
If you have checked the blower motor and it does function when power is applied then I would suspect the Blower Motor Resistor Pack is defective. It is also possible the blower motor speed control is bad, but highly unlikely.
If the blower motor randomly and intermittenly quits and does not work, chances are good the blower motor itself is faulty, if the blower motor does not work on all fan speeds from low through high, it most likely needs a blower motor resistor.
Probably a bad blower motor resistor
The blower motors only work with the engine running. If the blower motor has three wires on the electrical plug, then the blower motor module is built into the unit & it's very expensive. Sometimes, you can tap on the motor with a hammer & it may work or slowly turn. If this is the case, replace the blower motor.