I had similar problems with my long-term CC. I mostly loved that tractor, when I wasn't cursing at it for the electrical problems. I got it at a great price because the original owner couldn't keep it running and the $300 service calls to the dealer got too expensive.
I got it running easily but as everyone knows, there are several interconnected switches which can randomly affect the ability to start and the PTO to engage. The PTO switch is the worst offender. Over the years I had it, every electrical switch and connection on the machine failed intermittently. Replacing with another OEM switch only fixed the problems temporarily; they'd reoccur the next year or the next. The only way to make the tractor reliable was to rewire the machine and use an industrial-quality aftermarket starter switch and a simple on-off pull switch for the PTO.
And yes, the above is only my solution and not the recommended one; removing the lawyer switches makes some people uncomfortable, so don't do it if it will worry you. Just live with never knowing if it will start, keep running or complete the work.
Another FWIW - the "safety" function of having the PTO disengage when reversing and continually re-engaging it at high RPMs will drastically shorten the life of the PTO. Again, if an operator doesn't feel safe backing up with the mower running, then leave it as is and replace the PTO clutch as needed.