I just had the same problem. I tracked it down to the BCM, the small white plug to the far left has 6 wires in it, the red one goes to the cluster lights. mine had 5 volts on the red wire all the time while all the rest of them went from 0-12 with the dimmer. IIRC the brown wire with white tracer came from the dimmer. They all had 5 volts when the lights were off. I guess there is a chance these could be the same on an 06 truck. It was gonna cost 510+tax to replace the BCM, so I just put a jumper wire from the brown/white wire to the red one. I probably should have cut the red wire between the jumper and the BCM, but so far its working ok. Save the real problem for later, you know.
Some other suggestions I got were:
Check Ignition Switch
Check headlight switch
Check ground connections
Check cluster
I tried a different headlight switch and a different cluster before tracing the wires to the BCM and checking them there. I also tried my cluster in another truck to make sure the problem wasn't in there. I had tapped into the red wire @ the back of the cluster for the light in my boost gauge, and I don't know if that had anything to do with it or not, but I unhooked it anyway. I may go back and use it to switch a relay for gauge lights sometime.
