It sounds like someone has monkeyed with the wiring for one thing as sitting on the seat is not supposedly affect the starting; unless, there is a loose connection as the seat switch according the diagram posted only affects the magneto.
To me it sounds like someone has wired the seat switch into the starter circuit provided the seat switch is a N/C switch.
As it refusing after use of the deck it does sounds like a bad PTO switch. They do mess up this as they don't make contact due either dirt or wear.
Side note in reference to following comment.
Checked ignition switch, as predicted, when in "run" position, M and G have continuity.
If this engine has a magneto ignition system they are normally not conducting in RUN position as here they are use here to kill the magnetos. Which would needing to connected in the off position. This indicated by the seat switch being grounded on one side.
Now this all depends if I reading the wiring diagram correctly. It leaves a lot to guess at when compared our normal wiring diagrams here.
