If your AC isn't working, the problem isn't a cycling switch, but likely one of these:
* Low refrigerant: This is the most common cause. The system needs to be checked and recharged by a qualified technician.
* Compressor clutch failure: The electromagnetic clutch that engages the compressor might be faulty.
* Blown fuse or relay: Check the owner's manual for the location of relevant fuses and relays related to the AC system.
* Problems with the climate control system itself: This could be a faulty sensor, actuator, or other component within the system's electronic controls.
Instead of looking for a cycling switch, take your Silhouette to a qualified mechanic or auto AC specialist to diagnose the problem.