Sounds like you have badly fouled sparkplugs.
Pulling the coil wire partly out makes the coil build more voltage to fire through the increased gap of the partly pulled coil wire. This higher voltage is able to fire through the plug fouling.
Clean and regap or replace the sparkplugs.
It's an effective trick to remove the plug wire on a misfiring cylinder with a fouled plug, hold the wire a fraction of an inch from the plug terminal so the spark jumps the gap. This will often get the fouled plug firing so combustion heat can burn off the fouling.