Set your tester to continuity-test. Better yet, if it has a beeper that sounds when there's continuity.

The fan switch is just a switch. It closes the circuit between it's 2 terminals when it's hot. So it should have no continuity when it's cold, then suddenly it has continuity when it's hot.

Best way is put it in a pot of water with a thermometer. Then you heat up the water & measure the temperature when it switches 'on'.

You can also jumper the fan switch wiring plug with a paperclip. Key on, that should make the fan run. If this works, you'll know the rest of the system (fuses, relays, wiring, & fan motor) is OK.