The RH pedal (aux brake) has a limited purpose. It was useful on the models before smooth-start clutch, which came along in the early '80s. It was to prevent the mower from rolling downhill backwards while letting the clutch out. The older mowers had a snap or jerk to them when they engaged and would easily rare up, especially on a hill. The advent of the smooth-start clutch pretty much eliminated the need for the auxiliary brake and it was soon eliminated.
