I disconnected the third brake on my '06 2LT because, well just because. My cruise will work MOST of the time. The other day, my cruise quit working but, my traction control light came on a little later. I found a crank position sensor code when I got home. But, it did this previously and then started working again after I shut it down for a little while. I'd been having a "#4 cylinder misfire" issue also, which may be related to this issue. I had an '07 that I did the same with and had NO issues with cruise with that one.

 

I moved this from a 10 year old thread.

Cruise control might not function with some codes. Like a P0304

 

The cruise control requires the CHMSL to be activated once before it activates. It works by measuring the resistance of the bulbs. TCHMSL is a FEDERAL mandated safety thing, it is not legal to deactivate it.
Your traction light came on because of the misfire, not related to the CHMSL.
The CEL is there to alert you of potential harm to the expensive cat. Why ignore them? Being that it is intermittent it is probably just a loose wire.

 

Re-connect your 3rd brake light, and maybe avoid being rear-ended.

Some have put in an LED replacement, but that may require an added bypass resistor or the high impedence will make the BCM think the bulb is missing or burned out and punish you with Inconvenient Remote Start Denial (IRSD*.)

*Not an official term. I made it up.