"Pressure is related to volume temperature and a constant related to the substance being compressed by PV = nRT. "

Isn't that some of that Ideal Gas Law stuff? As a practical matter, does it really have any relevance to hydraulic brake systems other than possibly theoretical?

" Just like an open garden hose vs. one with a smaller opening, for the same volume of fluid, the pressure is higher."

As long as one end of the hose is open, I see your point, but once the brake pedal is depressed and the fluid is static, the pressure is everywhere the same regardless of line size. Cap off your garden hose to stop flow, and check pressure at the input and output. Would it not be the same at both points for a static fluid whether a garden hose or brake system?

Bob