I thought I knew how our TPMS worked until... I had to get a wheel repaired. We took the tire off and removed the sensor. I through it in the trunk and put my spare on. Drove home (about 6 miles). Light never came on. ??? Wheel repaired drove back the next day, remounted sensor and tire all good. A few day later it's 28* here. TPMS light comes on. I check each tire and top one off. Lights been out ever since. My assumption was that the light should come on if any of the sensors programmed to the car detect low PSI, but this didn't happen for me. Yet, I know it's working because the light will go on if I drop pressure and start the car... and let it sit. Put air in that tire (random tire) and the light goes off within 1 to 2 min. So not sure why I didn't get my light driving home on the spare that day.
I'm willing to go aftermarket on a sensor, but would expect to pay something for programming.. nominal fee, whatever. While I do check my pressure regularly, I think TPMS is a good thing and worth fixing if not working properly.