Buck, my
M59 had a similar lag time or hesitation for a few hours....and then the throttle cable from the foot pedal broke. That cable is a stranded wire type working in tension to control the engine RPM so that the RPM matches the foot pedal's opening of the servo valve to the HST. My suspicion is that as the cable began to fail it was stretching just enough to lose the registration between RPM and HST valving. I wonder if that is what is happening with yours? It's hard to tell, though. If so, it's no biggie.
It could be hard to tell if a failure is happening because mine failed inside the rubber bellows that protects the wire cable from dirt. You might try laying under the tractor's right side, double-jointing your wrist, and then try to feel of the wire inside the protective bellows - see if it feels intact...., but I'm not sure you can tell anything that way. As I recall it's not possible to retract the rubber and actually see the wire. It's not the kind of thing anyone would normally check and not made for easy access.
From an engineering standpoint, Kubota did do a good job routing that wire, protecting it from dirt with a rubber bellows, pre-lubing, and also they passed it over a proper diameter drum so that the strands wouldn't fatigue in bending. The only problem is that the wire itself turns out to be slightly undersized for the load. That became obvious when I took mine off and looked at the break under magnification. It is a pure tension separation. However, ours is an early
M59 and Kubota may have redesigned that part by now.
Old style
M59 owners might want to keep a new throttle cable in their spare parts kit. Not expensive, and it's about a 30 minute job with hand tools and fingers to swap it out. The good news is that if yours does break you aren't absolutely stranded. It's awkward, but you can use the hand throttle to finish up and get home.
luck, rScotty