I have a cheap Rocboc solar TPMS, with 4 external sensors I use on the back duallys on my little Toyota.
While the pressures and temperatures reported are not NASA accurate, it never fails to report low pressure. Because the system is cheap $40 or so I did not trust it and tested it numerous times. loosen a sensor and it quickly alarms. Take a sensor off, pressure goes to zero and system alarms, within seconds!
My wifes Honda Fit has TPMS, does not say witch tire is low. So I added a Carchet system to her car and it is about the same. The Carchet has the advantage of being able to buy replacement sensors. None of the other cheap ones have replacement sensors available.
Both systems are a pain to program and the instructions are dismal, ya get what ya pay for.