Hi X.XXXX
Welcome to Just answer,
I assume they are referring to the opposite of "hot" side, the hot side is power in, this would make the "Cold" side power out to the brakes. which would make it the dark blue wire.
This vehicle may be equipped with the seven-wire trailer towing harness. This harness has a seven-pin universal heavy-duty trailer connector that is attached to a bracket on the hitch platform.
The seven-wire harness contains the following trailer circuits:
Four-Wire Harness (Trailer Brake Controller)
The brake harness you are referring to is the stop lamp switch.
This is not the trailer harness.
There should be a blunt cut harness under the steering column area with the 4 wires, these will be taped to a harness with four wires that are cut and nothing connected.
I am searching for a diagram for the location. but wanted to send this so you could look to see if you can find it.
ASE Master Tech/Instructor
20 yrs Experience; GM factory Training ASE Master Certified with L1 advanced engine diagnostics