I have a 2003 Silverado LT Z71 with the digital temperature controls. If you select the "AUTO" after the truck reaches the set temperature. It starts to make a clicking sound. If you set the air to flow out the front of the dash and at your feet the clicking sound disappears(sound is coming from drivers side). I have heard about replacing the actuator and also about having it reprogrammed. Has anyone else had this problem or had it fixed???

 

Never had luck reprogramming. GM TAC has us reclock the iternal sensors sometimes. Had best luck with replacement.

 

I don't mean to sound like you aren't the brightest crayon in the box. (I am probably wrong as it sound anyway), but are you sure it's not the compressor kicking in? If not see what is on the driverside for air conditoning. Or vents for that matter. Other than that I can't think of anything off the top of my head.
Sorry if I'm no help.