Yep. Check seat switch.
It's off that you are having multiple safety failures.
Prior to clarification, I was assuming you mis-diagnosed the problem the first two times thus the neutral and PTO switches got replaced. But those two switches only cause a no-show or only cause a shutdown if butt ain't in seat.
You don't have to be In The seat to start the tractor, so clearly all the safeties related to starting are working since it starts. But to move tractor or start PTO, it has to detect operator present.
However the seat switch is a two part switch. So it's not just a simple 2-wire continuity test.
Try this....start tractor. Leave in neutral with brake set. Engage PTO, and immediately flip seat forward. What happens?