It is almost always caused by a too lean pilot jet circuit. That means the brass pilot jet metering orifice (at the center of the end of the jet) and the pilot adjusting screw is slightly gummed up. The pick below is for the EF1000iS, but it is similar to the EF2000iS. To remove the pilot screw for cleaning, you have to remove the plastic limiter tab on the screw cap itself. I would either cut it off with a small Dremel cut-off disc -or- melt it away with a soldering gun. DO NOT cut it off with a knife or a pair of Dykes (wire cutters). Why? Because I found that the brass screw shaft has a very small necked down diameter under the plastic cap to punish people that try to force things, even just a little bit! Immediately after removing the tab, turn the screw IN slowly, counting the turns, so you know where to reset is as a starting point.
IMPORTANT: Be sure the carb's throttle plate tab is pushed all the way to the full throttle stop after remounting the carb (if removed) so the throttle stepping motor is correctly set. After the engine runs again with ECO idle immediately ON, after 2 minutes running (for ideal adjustment engine temp) set the pilot screw by turning it in (CW) until it falters and RPM cycles, then turn it out (CCW) until the RPM is stable and "sounds smooth".
If it still cycles you may have corrosion in the pilot jet metering orifice, something only "mechanical cleaning" or replacement can cure.