As it is a JD you have the benefit of the absolute best written most informative & easiest to use repair manual ever written for a lawn mower.
Down side they are about 1/6 the price of a JD service at a JD agent .
From what you are saying sounds like a worn safety switch , dirty joint or wire broken off at the crimp which is making occasional contact.
AFAIK the seat switch is not in the cranking circuit.
The parking brake switch is behind the brake lever & the lap bar switches are under the lap bars.
The manual will show you the location of every switch.