Brakes

Normally when pumping the pedal brings it up, it is because the rear drum brakes are badly out-of-adjustment. Each pump runs the shoes out a. Little further, but it can take a good five seconds for them to slowly retract under spring pressure, Your next pedal pump comes before the shoes retracted, so each pump runs them out further. The pedal builds pressure once the shoes have contacted the drums. The clue is the pedal will be low again once you release it for at least five or ten seconds.

That is not the solution when you have rear disc brakes, and a lot of cars today use them with anti-lock brake systems. You can get the same symptom though, like you described, when the reservoir ran empty during bleeding, or in your case, when the master cylinder was replaced. You likely have a system that requires a scanner to command the ABS computer to open two valves so those chambers can be bled, then you will have to bleed again at two wheels.

If this is what happened, I have a trick that makes bleeding at the wheels unnecessary when you replace the master cylinder. I can describe that if it becomes necessary.

Be aware too that GM and Ford used a miserable rear caliper design that had the parking brake built into it. Those pistons do not self-adjust out by just pumping the brake pedal like the front ones do. Those will only reach their initial adjustment by working the parking brake repeatedly. If a cable is broken or rusted tight, you can use a large pliers to work the lever on the back of the caliper by hand until you feel the resistance build up. Once that is achieved, they will continue to self-adjust like the front ones do. When those rear ones are not adjusted, you will have a low pedal. Caliper pistons do not retract like drum wheel cylinder pistons do, but they do retract very slightly due to the bending and straightening of the internal square-cut seal. If one piston is close to being in adjustment, you can get a brake pedal that pumps up, similar to when shoes are out-of-adjustment. You still need to do the manual adjustment though.