No power at the plug in any of the illumination circuits in the door, HVAC controls or radio? My thought is that it has to be BCM related, one of those modules has a short or a direct short.

If you want you can try this.
Unplug everything that does not light up. Disconnect the battery wait for 30-60 seconds. Reconnect the battery. See if you have power to any of those illumination circuits.
*If illumination power exists at the plug, then plug each one in until the other does not work. That would be where the fault is.
*If not illumination power exists at the plug, then it's a BCM or direct short.

I'm giving you the troubleshooting that I would do in your situation.

 

Thank you for the direction... any idea which wire provides the backlighting for the (1) headlight switch assy, (2) climate control assy, and (3) 4-wheel drive/traction control assy? I can't find a pinout diagram the check them out. The only one I've found was on here, but was for a 2005 H2 I believe. Wouldnt imagine that they are identical.

 

All h3 model repair manuals free download here

https://schwarttzy.com/h3-hummer/

 

Thanks BruceS, but I've downloaded these long ago. Within those manuals, the diagrams for the systems that I'm not getting back-lighting with state that the supply wire is gray. After visual inspection of all of the systems that I'm having issues with and their corresponding harnesses, there is no gray wire contained within them. That is what prompted my starting this forum discussion.

 

I bought a used 2008 H3 Alpha and I’m experiencing the exact same condition. I also have an aftermarket stereo, alarm, and remote start system.

I have not tried a new dimmer / light switch assembly yet. That’s next.

 

Let's try to avoid digging up OLD Threads please. Thanks in advance. READ: Old Threads/'Necro-Bumping'

 

Dyno.... My setup is similar in the aftermarket head unit, remote start/alarm etc. My issues turned out to be multiple, simultaneous components failing. Light switch, climate control switch, traction control module all had failing bulbs in them. Regardless of what you may read, they are able to be removed and disassembled to access the bulbs themselves. Some simply have the locking notches holding the bulbs in, while others are soldered. I went the route of replacing the assemblies as a whole and now I'm good to go.