As far as I know, the so-called “evaporator thermostatic switch” isn’t actually a switch; it a temperature sensor on the evaporator that’s connected to the engine control module which, in turn, controls the operation of the AC compressor. If the temperature at the evaporator gets down to near freezing, which can cause ice to form on the evaporator that would block the air flow, it turns the AC off until the temperature is high enough to prevent ice build up.
Icing of the evaporator can be caused by low refrigerant in the system, or even a blocked cabin air filter that restricts air flow.
What did the mechanic do to come to the conclusion that the “evaporator thermostatic switch” needs to be replaced? Was the level of refrigerant checked with manifold gauges?
Was the cabin air filter, and the condensor, checked to see if they might be clogged?
Did they check the AC compressor relay?
Incidentally, the AC is turned off if the engine is overheating, or under heavy load (such as when accelerating with the pedal way down) to reduce the AC load on the engine. So sometimes the cause of the AC cycling isn’t the AC itself.
I don’t think the symptom, as described, can be diagnosed down to exactly what part is bad; there’s not enough information.
Do some searching and reading here; many AC discussions are about on/off cycling and the possible causes.
