I have a 2006 GMC Sierra. When the button for the inside air recirculation button is on, the clutch for the air conditioning compressor cycles on and off and cools down the truck cab with out the air conditioning button being on. One time neither the a/c button or the inside air recirculation button were on and the air conditioning clutch was still cycling on and off.
It seems to be an electrical problem, but what is the most likely component that is malfunctioning? Appreciate any info.

 

My money's on the control panel. Seeing that your A/C system works, it just never seems to stop with the A/C request. Either that or it's a PCM issue.

I'd recommend getting a new control panel and swapping it in there, if that doesn't fix it, easiest thing to do is take it to a dealer and have them diagnose it.

 

Inside recirculation will always engage the clutch.