The one and only time the TPMS light was lit on my dash ? I checked all the tires on the ground ~ they were all fine.
Then it dawned on me ~ I checked the spare tire and it was low.
I aired it up ~ it's all good now. There is a TPMS unit installed on my spare as OEM.
I have a 2005 DC Tundra with the tpms light on. I took it in to Midas and they put all new sensors in (including the spare). They said the batteries in the sensors sometimes fail. They checked with a meter and all 5 sensors were sending the correct signal to the computer. The light is still on. What gives? They couldn't figure it out.
Depending on how old the spare is, you might need a new tire as the spare. I had the same problem. I could add air to bring the tire to proper pressure, and within a couple of weeks, the light would flash. But, to answer the original question, yeah, they put a sensor in the spare.