First of all, what engine is fitted ?
Second, follow the wires from the battery.
Usually they go directly to the starter solenoid then there is a tap line off the hot wire that goes to the B ( battery ) terminal on the ignition switch.
Very commonly people replace the solenoid and neglect to connect this wire and that usually has the fuse on it.
Next safety switches all look the same but they are not.
Some are open with the pin in while some are closed with the pin in and a lot have both types in a single switch.
However again, there is no connsistancy and the position of the terminals for the normally open & normally closed side of the switch can be either top or bottom.
Toe circuits in operation when cranking ( or not as the case may be )
1) solenoid power wire - B terminal on ignition switch -S terminal on switch -PTO switch-parking brake switch - + trigger wire on solenoid. Cranking circuit
2) ignition switch -parking brake -lap bars - magneto kill circuit ( some times also seat switch ).
because people keep on bypassing the safety switches cause they are so much smarter than the engineers who designed the mower, if the mower has a 4 pole ( active ground ) solenoid, the kill switch circuit can also be hooked up to the ground wire for the solenoid either directly or via some relays.