It can be a confusing system.
I think that's why so many people convert to vacuum - because it can be so confusing, and if you don't "get it" you'll forget it.
I get it, but I'm an electrical engineer in the fluids business.
You've seen this diagram:
http://www.gnttype.org/techarea/images/PwrMstr.gif
It may help you understand more what makes the light come on.
The pressure switch is setup to trigger the light when the pressure is below a certain point - usually when the motor either can't keep up or just isn't working. It also turns the motor on and off at different set points - above the low pressure set point. The problem is that the low set point is usually too late.
If the pedal gets hard, the pressure in the system is too low.
It is up to the mechanic to figure out why.
1 - the pump isn't working - why?
2 - the acc is dying - time to replace?
3 - the switch is faulty - how do you determine that?
4 - the system is internally leaking - Seals or check valve?
The diagnostic tests give you time intervals.
They have to be interpreted.
There are many points to consider.
Does this answer your question?
It's a purely mechanical system.