My 15hp Kawasaki sometimes requires the accelerator pump to come on to keep it running. No matter what RPM the throttle is set at the engine will go up and down in RPM depending on the relative position of the throttle.
Is what you're saying that with the engine at a fixed setting, the RPMs will go up and down instead of remaining constant? If so, this "hunting" can be caused by a lean air/fuel mixture usually caused by a blockage in the low or high speed fuel circuit. Does the engine smooth out if the choke is engaged a bit?
What does the fuel look like? Usually, if a jet is plugged the problem doesn't go away, but old gas can sometimes cause intermittent problems. Does the hunting occur more often when the engine is first started?