I have been having the same problem as you describe, it is also a '07 613. After I read your post I tore my dash out and checked the switch that you described and cleaned with contact cleaner, while this did not solve the problem, what I did find is that the on/off switch circuit for the a/c is the source of my problem, it is a printed circuit board with a couple of resisters and a timer(which is the "clicking" sound you hear) to cycle the compressor, I beleive one or more of the componants is bad or weak, although it is probably pricey I feel that the heater/ac control assembly should take care of this problem. I currently have the compressor on a switch so it works however you need to turn it off occasionaly to keep from freezing the system. I have been trying to find this problem for 2 years so I feel your pain, what i might try next time I have the truck home on a weekend I am going to try to remove the on/off switch and solider another switch and see if that takes care of it if I can't get the shop to get me a new control. GOOD LUCK!!