Kawasaki 19-hp FH580V engine suddenly started running rough when hot.

I have a Kawasaki 19-hp FH580V engine on a Graveley Promaster 44Z mower. Both have worked flawlessly for eight years.
Suddenly, the engine has started running rough after running for approximately 25 minutes. If I let it cool down, it runs fine again while mowing for another 25 minutes or so. I repeated this pattern three times.

I think the fuel is fine. The mower has two tanks. The hoses hat draw fuel from the tanks don't appear to be cracked and the screens are clean. The air cleaner is clean, though I plan to replace it. Fuel is visible in the in-line fuel filter, but I plan to replace that also.
I haven't checked the plugs.

Could the problem be a coil or a poor electrical connection or ground?

Would a fuel pump problem come and go like this?

First you need to find out why it is getting too hot. Remove the engine cover and clean it. Then see if it happens again. Also look for anything blocking air flow around the engine compartment.

The problem could be a coil, an inductive tachometer that clips / hooks or wraps around one or the other spark plug wire would likely diagnose this with ease.

One would think, if the problem were a poor ground / electrical connection that the problem would be present at all times.
Ditto with the fuel, however it is also possible the choke isn't opening fully anymore, I'd check the linkage and make sure it's moving and then make sure the butterfly valve is full open when the choke button / handle is in the open position, in case of automatic choke you'd have to wait for the engine to warm up.