My '02 Ranger (automatic trans.) will pull to the right and the break pedal “gives” when coming to a complete stop. This happens pretty much all the time now but started after the vehicle had been sitting for a while. (overnight or during work) It seems to happen just as the truck engages the lower gear before stopping.
Is the breaking system related to the switching of gears?
I think you have a failed right brake caliper.
I agree, but you could make a case for either caliper. The sudden increase in vacuum as the transmission shifts down is increasing the power assist of the brake booster. There might also be an issue with the brake booster’s one way valve in the vacuum line.