AtlWrk said:
HVAC-B feeds the logic of the main hvac control module and the auxilliary control module in the center console. If you can get to one of the modules and unplug it you could isolate which one is having the problem. Not sure which one would be easier.
Problem found!!! It turns out that I have a faulty auxilliary control module. (This is the HVAC module mounted into the center console that faces the rear seats and allows the backseat passengers to control their climate.) As AtlWrk suggested, I disconnected the rear climate control module - which after some experimenting turned out to be pretty easy since the control module simply pops out of the rear console with a little help from a small flat screw driver. Once the module was outside the console I could easily disconnect the wiring harness feeding it.
With the wiring harness disconnected I tested the draw with my multimeter and after a couple of minutes the draw dropped below 0.00 amps. Just to be sure I plugged the module back in and the amp draw went up to 1.75 - 1.80 and held constant, indefinitely. After 30 minutes I disconnected the rear HVAC module again and after a couple of minutes the draw, as expected, dropped below 0.00 amps.
I just looked at e-Bay and can find a used, warrantied rear HVAC control module for $39 plus shipping. Considering that I've only used the rear temperature control module about 3 times since I bought my '03 Envoy new it's no big deal if I ever replace it.
Now I can leave the HVAC-B fuse in while the ignition switch is off and not worry about waking up to a dead battery. Thanks everyone for all your help!! :wootwoot: