Temperature sender sends signal to PCM which decides when fan is to come on. Hi-speed if a/c on, lo-speed for normal coolant temperature increase. I believe hi-speed also comes on if excessive coolant temp is reached.
In you car hi-speed relay feeds fan motor directly but the low-speed feeds thru' a dropping resistor (the part you have puchased).
You don't state location but, if warm enough, you could turn on a/c and check hi-speed fan operation. Alternately pulling the relays and jumpering the appropriate relay socket terminals to simulate contact operation is a means of checking. Latter procedure requires substantial jumper wire and battery covered with towel as precaution.
Underhood wiring harness has a long extended warranty and the heater fan switch and dropping resistor a shorter one.