Then neither of the two service manuals I have here cover the 3 pole brake switch.I believe that mower uses the 725-04232 switch for the brake. The switch snaps into a cutout and is non adjustable and the switch is fairly expensive. They are prone to not having the plunger pushed in far enough when the brake is applied. Wiggle the brake lever and see if it starts. If it does you need to modify the switch. The switch is a PITA to get to.
There are different versions of the RZT50. Some use a 2 pole brake switch and some use a 3 pole brake switch.