Mower ignition is self generating,
The fuse will be on the red wire going to the ignition switch.
The energising wire to the starter solenoid goes from the hot wire to the ignition switch ( via a fuse usually ) then to the PTO switch, then to the gear selector / speed controller then on to the brake / clutch then finally to the starter solenoid.
Just to make tracing it hard, it usually changes colour every time it exits a switch so you really need to get a wiring diagram.
YThe ignition wires are all earth wires , be very careful not to accidentally apply battery voltage to any of these wires as it will fry the igntion module.