Something is grabbing in rear only in reverse when cold

This is very common,
The cable can build up rust and not release after it is disengaged.

If you can slightly jack up one or both rear wheels on level ground and put your arm just behind the rear wheel at the axle and you will feel and see several lines going to the back of the wheel.

One will be a thin steel tube ( hydralic line) NOT IT.
Another will be a flexible cable going into the plate behind the rear wheel
THATS IT !
You should be able to see the cables if you get on the ground under the rear bumper. The cables should run arcoss the axle to each wheel.

Grab it and pull back and forth real hard several times and it should release then do it to the other side. (Don't grab any electrical wires).

Make sure you have somebody with you when doing this.

https://www.justanswer.com/car/1bpzv-release-emergency-brake-1999-buick.html

sounds like the tracking rod may be broken or loose.

This is a common problem. Remove the drums, and clean out the brake dust with brake cleaner and readjust the brakes.

Sounds like you have sticking caliper pistons, have you ever changed brake fluid? Replace calipers and flush brake fluid and clean ABS sensors with
ABS safe brake clean.

bad transmission, it will need rebuilding or replacement. sorry....hopefully this helps

How about the rear bearing? These cars do have them!

It sounds like the brake shoes are reversed or the wrong ones. Also may be faulty, or incorrectly installed brake hardwre. I'm assuming this problem did not happen until after the brake job? If it did, then you might have a different problem.

You are probably correct in thinking its the wiper motor. You can do this but you will need to remove all the interior trim from the rear hatch first. Get a trim clip removal tool at a parts store...it will work much better than just a flat blade screwdriver. You'll have to remove the trim panels starting in order from the top of the door, then the left rear window side trim, then right rear window side trim, then the grab handle, and finally the main rear hatch trim panel. Once inside, removing and replacing the rear wiper motor is easy. You'll start by lifting the cover on the wiper arm retention nut. Remove this nut to get the wiper arm off, then remove the nut under neath which is the motor shaft mounting nut. Now, back inside to remove the other 3 motor mounting bolts. Don't forget to disconnect the connector for the motor wires. Reverse steps to replace.

reverse requires more hydraulic pressure to hold it in reverse. Maybe you have a partially plugged filter that the thicker, cold fluid can't get through. The whirr could be the pump in the trannie being dtarved for fluid due to being plugged. Otherwise, you may have a bad clutch or band for reverse that requires a trans overhaul. good lcuk.

Yes, it definitly sounds like a fluid problem. However, did you know that there are different weights of rear end lube for different rear ends? I would advice going to the dealership and asking what weight they show for your rear end. You need to first copy the tag # off the rear end so that they can be sure which one you have.
Bill