Always go off of the vehicles certification label in the door jam. The car goes through alot of vehicle dynamic testing to develop the appropriate characteristics that allow for the optimized condition. There are a few times when I would slightly adjust that thought process...in winter with ice, I drop a pound or two. For long highway trips I add a pound or two and for towing, I add about 5 extra PSI to the rears.
As for TPMS...the system you describe sounds like an indirect which uses rolling radius and possible the tire harmonics to judge tire pressure. These systems are run through the ABS/Stability modulator, using the input from the wheels speed sensors and an algorithm to judge the pressure. Regulation has an allowance of 25% below the cert label pressure to set a light. When you push the button, it begins a calibration sequence that can take a long time to complete.Hence the inconsistancy of the light.