2006 Ford Fusion soft brake pedal

2006 Ford Fusion 2.3 new car to me with soft brake pedal issue.

Car is new to me and don’t want to spend a ton of cash throwing parts at the problem.

If you pump the pedal 3 or 4 times it gets okay and will stop but when you release it has to start over. First thought is air in the lines but my son and I bleed the brakes 2 times around the car starting at back rear and it makes no difference. Then thought maybe bad fluid so took out all from the master and replaced it, bleed the system 2 or 3 more times making sure to let a lot of fluid escape but still no difference. For bleeding here is how we are doing it, I have him pump the brakes 4 or 5 times and hold, I brake the line loose fluid comes out I tighten screw, tell him to pump up again. We repeat 3 or 4 times fluid is clear no bubbles and move to next wheel. Might try the bottle hang method tonight.

I know the left rear caliper piston is sticking it moves on the pins fine but the piston doesn’t move very much. Maybe this is causing the issues I have a new one ordered but never seen a caliper cause anything like this.

Thought about buying one of the vacuum pumps for bleeding brakes but not sure that will get me any closer.