Now for the Model S:
Someone above made a very good distinction:
If your TPMS NEVER showed tire pressures in the display. (AND you are not using hacked programming
to show tire pressures) You have a Gen 1 Baolong system.
The Baolong system in Model S is considerably simpler than in the Roadster.
2 antennas and the ECU are combined into a single part ECU/Antenna combination.
This is part number 1004624-00-D or other letter revisions.
This part memorizes the sensor addresses and also must be programmed by the Tesla TPMS Tool.
This time the tool delivers the programming on the CAN bus - The tool is attached to a diagnostic connector
below the main display.
When your TPMS sensors' batteries expire the sensor needs to be replaced.
Imagine if you will your tires' addresses are: A, B, C, and D.
They are memorized in to the ECU/Antenna when the car was first manufactured.
If you have these cloned and replace them with A, B, C, and D in their respective locations
there is no need for reprogramming, a button, or the Tesla tool.
The addresses are the same as they always were, they stopped working, and now they work again.
HOWEVER if you replace them with new pre-programmed sensors with addresses E, F, G, and H
the car has no idea what these addresses are or where they are located.
The Tesla tool is needed to update to the new addresses.
The Tool "wakes up" the sensors and tells them to report.
Imagine all 4 new sensors report their addresses - the car reads 4 addresses but has no way to determine
their location in the car... that is why the Tesla tool is necessary for new addressed sensors to assign them
to their proper location.