Look at the eyesight at reciever/drier..if it is foamy, you are more likely to be slightly short of refrigerant then to have a bad sw. If so, just a topping off usually takes care of that. If one has decent a/c cabin temps ,but not enough pressure on the high side to trigger the sw, it needs only a few ounces added to get to fan cut-in spec.......also be aware that one can also have the correct charge and no low fan if the AMBIENT temp is low..high side pressures do not get that high at low ambient temps and that condition is NORMAL..aux fan is only called upon at high thermal load conditions ..unlike many cars , the low fan does not ALLWAYS run when a/c runs, but rather , only when the systems is being taxed. The fan circuit is only there to keep the high side in check from runaway high pressure by adding airflow across the condenser..that cut-in spec is considered in it's design..and often mis-understood.
I see many guys change the switch and then claim it was the fault b/c the fan now works ..of couse it now works..you just got the refrig. back up to full charge when you changed the sw..a topping would have done the same ...the difference would only be in the $$$$$ amount it cost you..