I believe it works by wearing through the little nub of the sensor as it reaches the wear limit, and then completing the connection triggering the warning.
If the sensor is missing, or broken as yours is... there is nothing to trigger the light unless the circuit is completed. A broken sensor appears the same to the car as one on a good pad. The sensor itself is consumable and only a few dollars. You should be able to verify the function of the warning light by completing the circuit yourself, but you'll have to follow the reset procedure to get the light to go out.