Well you have come to the limit of what I can do for you without a wiring diagram.
IT sounds like the power wire from the hour meter to the solenoid has an internal break, but the hour meter should not be connected to the starting circuit so it does not make sense to me as you are describing it.
The seat switch and the parking brake switch work together to kill the engine so you can get off with the parking brake applied and the engine continues to run.
But if you get off without the brake oapplied the engine dies.
The parking brake and the motion control levers ( both of them ) are connected together as well so if you try to move the mower with the brake still applied it will kill the engine.
All of the above are earth ciricuts so you are checking for continuity or open circuits at these switches, not power.
Sounds very much like the parking brake switch is faulty but as stated above I have no wiring diagram
I have tested the brake switch and it is faulty either that or there is a ground on the other side of the circuit. When I tested the plunger with a test light it will stay light up while depressing it. About a quarter of the way down it will briefly kill the test light then come back on and stays on in the fully depressed mode. If I'm thinking this system correctly it should release the ground when the plunger is all the way extended which is parking brake off.. The thing I don't get is why there is no crank signal I have traced the orange wire at the key start signal to the hour meter I get a signal to start there but nothing coming out the rest of the wires are grounded by the drive handle switches. I ordered a switch will see if that fixes it but I think there ar 2 issues. Thanks for the response.