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Did you check the two arm switches? If either arm switch is stuck open, the run circuit is not completed, the mower thinks there is no one in the seat, and kills engine.
Mounted on the frame , where each arm can push them when in neutral. Need the model number to find picture and show part. Do you have access to parts book?
I don't find them shown in electrical, but see # ***** passes over the pushbutton switch, one mounted on each side of the frame!
see question is still open, did you find the switches and check them?
Did you check the seat switch with ohm meter to see if it is making and breaking?