They will trip at +- 10% (~3.5 psi). generally, driving around will make it go off. It took ~75 miles for mine to re-set last month after a top-off.

If the battery dies, the sensor dies with it, Replacement time. (See below).

If a pair of sensors is swapped, (R/L tire rotation, for example) the light will come on. If this happens, a dealer is the only one that can re-sync these buggers.

I'm one of those that really is bothered by warning lamps. I get it fixed.

Good luck.