04 trailbazer and xk01

At this point if I were in your shoes I'd do whichever of the following 2 things was less aggravating/time consuming.

1. Get a replacement XK01 and run wires to the rear door triggers at the rear seat fusebox. It sounds like you have a defective module since it's not outputting anything to the door trigger and all other wiring is golden, so depending on where you bought it you might be able to get a direct swap.

2. Wire to the individual door triggers in each front door and to the 2 wires in the back hatch for glass/gate trigger, as well as to the rear door triggers at the fusebox. Obviously this means running long wires, much panel dissasembly and going through door boots as well as using 6 diodes.