When you load an engine by opening the throttle, the pressure in the combustion chanbers increases. This increases the resistance at the plug gaps. Any marginal component in the high voltage side can fail, causing the stumbling. Most likely it is a plug, a wire, or the cap.

Perform the "midnight test."

Be sure the underhood light is switched off, and switch off your interior light. Find the darkest location possible on the darkest night. Turn all lights off, and allow your eyes to dark-adapt for 10-15 minutes. (This allows you to see the dimmest glimmer of light.)

With the engine idling, open the hood and stare at the ignition components as you manually rev up the engine (turn the throttle spool). Everytime you open the throttle, it increases the combustion pressure. Rev the engine repeatedly.

Any breakdown of the ignition will be (faintly) visible as arcing. You can mist the ignition components with water to make the situation worse -- just a mist, not a flood.
--
Don Foster (near Cape Cod, MA)