When warm, the pto cuts out even when not going in reverse
Basically, a relay works, or it does not. You have other possible issues. You do not have a relay issue, that is a charging system or PTO clutch issue.
I suggest you check your charging system with the PTO engage and at High RPM to make sure the system is not dropping voltage as it gets hot. That would indicate the stator is choked up with dirt or the regulator is failing. The Flywheel has to be removed to clean the stator and checked for overheating.
Note: These have a bad habit of the flywheel magnets coming off with age. There are videos online about how to determine the magnets polarity and to reattach them with 2-part epoxy like J-B weld.
Cleaning the stator will resolve future issues, but the PTO clutch may be too far gone from overheating to be saved.
The next possible item is the PTO clutch air gap adjustment. With age and use the gap gets wider and the clutch magnet get to hot and cannot hold the driven disc. Some clutches are adjustable, and others are not.
I suspect the PTO clutch has been overheated too many times. The best way to test that is with an Amp clamp meter and see if it has a high Amp draw. That would indicate a failing pull in magnet.
This unit has a 1-1/8 crankshaft fit PTO clutch if I recall correctly. Replacements can be found on Ebay or several other online sources.