Okay, found some time to troubleshoot this a bit more. ecc_33, can you confirm these are the correct wires you mentioned in your previous post? These are the only ones that matches color and number you mentioned before at the BCM. I tested at these wires, between each other, the light blue is putting out 12 volts until you push the tow/haul button, which seems to cut the voltage momentarily. I am fairly confident in the light blue one, as I get continuity from it to where the light blue goes into the relay block. I also tried jumping the two at the BCM but no luck. Also, this switch works only as a momentary type correct?
Why did you jumper it with the light green wire??? That has nothing to do with the tow/haul switch.....
The tow/haul switch signal wire is the light blue wire only. The other side of the tow/haul switch just goes to ground.
So when you press the tow/haul button, it grounds that light blue wire momentarily.
The reason its reading +12v with the button not pressed is because of the internal pullup on the circuit inside the BCM that holds the input high (as seen by the BCM's microprocessor) until you press the tow/haul button, which "shorts" the input to ground, and pulls the signal from high (because of the internal pullup) to low (ground). The BCM's processor then sees this transition (it sees that input go low), and interprets that as the tow/haul button being pressed.
I think to go any further, you're going to need a Tech 2 to see if the BCM is acknowledging the circuit high/low transition. You've basically diagnosed the circuit as far as you can (wire shows +12v high with no button pressed, and then goes low when button is pressed, so that tells me that the wiring is all good)...
So now the only step left is to use a scan tool to see if the BCM is processing the input internally. Do you have another known-good BCM you can try swapping in?