It does not matter where the pressure switch is located when at static pressure. The internal system pressure is equalized, high side, low side , there is no difference in pressure. Static pressure only increases or decreases with ambient/system temperature, thats why its called static. The ac systems high and low sides do not have different pressures when the system is off. the pressure will equalize always.
All your statements above are 100% correct, but you are drawing the wrong conclusion as to what is allowing the OPs compressor to start, but to consistently drop out after a few seconds of operation.
Please reply where you think this analysis is faulty, or if you take issue with any of the statements:
1. OP states that when AC is turned on, compressor will always engage and run for a few seconds, then drop out.
2. The Toyota FSM tells us that refrigerant pressure switch will open if refrigerant pressure is less than 28 PSI, or greater than 455 PSI.
3. If the pressure switch is open, the AC Amplifier will prevent the compressor from ever starting, even for a second.
If statements #1-3 are all TRUE, we know that the system has 28 PSI or more of refrigerant pressure in the static condition, and the compressor will always start when the engine is running and the AC is turned on.
4. The static pressure (compressor not operating) in the system is equal at both the low side and high side of the compressor.
5. As soon as the compressor starts pumping refrigerant, the pressure at the compressor low side will decrease, and the refrigerant pressure at the high side will increase.
6. The refrigerant pressure switch is located in the high side of the system.
If statements #4-6 are all true, the refrigerant pressure at the switch can only increase when the compressor starts.
7. When the compressor starts, the pressure at the switch cannot decrease and cause the pressure switch to open.
8. It cannot be the pressure switch opening from LOW pressure that is causing the compressor to drop out after several seconds of operation.
9. If the system is grossly overcharged with refrigerant or the expansion valve is restricted, the high-side pressure could conceivably exceed 455 PSI.
The remaining two factors that would allow the compressor to start, but then drop out are:
a) The belt-slip detection scheme (compressor RPM mismatched to engine RPM because of belt slip) is cutting power to the compressor's clutch;
b) The pressure switch is sensing an excessively HIGH high-side pressure (greater than 455 PSI), which is cutting power to the mag clutch after a few seconds of compressor operation.
Situation (a) can occur if the serpentine belt is badly worn or oil contaminated, the wrong length belt was installed, or the belt tensioner is defective.
Situation (b) can occur if there seems to be a cooling problem, and someone just starts adding refrigerant to the system without knowing the total refrigerant charge weight, or without monitoring high side and low side pressures plus ambient temperature.