brake lights

Try checking the brake light switch.

Not totally up to par on Hummers but given today's environment of development in electronics, ECM's, BCM's, PCM's, modules and such, I would suggest a dialog with a Hummer mechanic or at least a GM mechanic at your local GMC dealership. Sometimes they, or that of the service manager, haven't a problem with people asking such questions. Other than that, if Hummers hold true to older GMC models, most of the exterior lighting is pumped through the mutifuntion turn signal switch.

The brake light switch was the problem on mine. Shot of WD40 and working it with my finger a few times cleard up the problem. You may need to replace the switch.

I had a problem with my tow package wiring (I think a short) which blew the board on the BCM, replaced under warranty. I dont know if i would have ever found it by myself!