Here goes:
From the key switch on the diagram, terminal "S", the flow of power goes through the "interlock" switch (brake pedal) on terminals 1 and 2. If the brake pedal is depressing the switch and it is good, it then goes through the PTO switch on terminals 1 and 2. Assuming the PTO switch is OFF and working, it then goes to the starter solenoid. The seat switch and reverse relay are not used for starting.
The tractor does not have a "neutral safety" on the hydro lever. That is what the brake pedal is for. With it depressed, it can't be in "gear". The reverse relay is a switch on the hydro lever coupled with a relay that kills the PTO when the tractor is in reverse. Seat switch must also be working for the PTO to come on. That series of tractor is a safety switch nightmare.