The engine shoud cut out when you get off the seat without the brake being on.
That is the whole idea of it.
You fall off & the mower stops.
Now getting back to your wiring photo
The green wire is a ground wire so should never show + 12 V.
If it does then it is connected wrong somewhere which is why the fuse was melting.
The Orange & white wire is the trigger wire for the solenoid.
A solenoid is just a fancy name for a switch, which is turned on & off from another switch.
Like all things DC it needs a + & a - connection.
The - connection is through the body of the solenoid & the + comes down that orange & white wire when you turn the key to Start.
Once the solenoid get a + & - it closes and send juice down the other thick red wire to make the starter crank.
To stop idiots messing with the safety switches they change the colour of the wires at every switch.
Follow the thin red wire on the hot side of the solenoid.
It should go to a fuse then the the B ( battery ) terminal on the ignition switch
When you turn it to start, the B & S are connected so + 12 Volts then goes to the PTO switch
If the PTO switch is OFF power flows through it to the brake switch.
If the brake is on power flows through the brake switch into that orange/ white wire and the solenoid closes and send power to the starter motor.
Below is page 84 from the CUB Service Manual which you can download for free from the CUB Cadet web site
On it you will see that ALL GREEN WIRES ARE GROUND WIRES so there should never ever be + 12 V on a green wire.
I will hazard a guess that some one replaced the brake switch with a wrong one .There are 3 different brake switches, they all look the same they all plug in but only 1 will work and usually fitting a wrong one blows the magneto chip cause it sends 12 V down the magneto kill wire.
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