New fan switch is a sensible move. If you want to test them, connect a multimeter on ohms across the contacts and place them in a pan of boiling water. They will go "click" and the resistance will drop to 0 ohms at the correct temperature. If the switch is specced to close at 96, it will need a few minutes in vigourously boiling water to operate. If it's fubar'ed no amount of boiling will get it to close, because you'll never achieve 100 deg C plus!
This technique can also be used to test the accuracy of the gauge sender. Remove from engine, extend wire from engine loom so you can get the sensor in a pot of water (a small camping stove avoids the need to park the Omega in your kitchen!), run a ground wire from the sensor body to the battery negative terminal, ignition on, heat water and see what the gauge reads. A thermometer in the water will allow you to calibrate it over a range of temperatures.
Kevin