Do you have an electric fan? If so, then there are a few things to check.
Have you checked the relays and resistors (check the plug in @ the a/c compressor* and the one in the relay box)? make sure that the relay in isnt "wobbling" in the box. I had that problem not too long ago.
There is also a fuse for the EATC - check that (if you have a digital climate control)
*I don't know if our trucks have a resistor on the plug that goes to the compressor. If so, check that. My buddy had the same problem with a 2007 Z06 corvette and that was the culprit. The resistors are like 1 dollar at radio shack.
Also, I don't know if there is a low side switch on our trucks but look for an electric connection on the lowside line somewhere and check that to.
that's all I can think of.