Yes the wire does go to the coil but if you want to put it elsewhere you can.
What is the easiest way to tell if only one cylinder is firing and which is having a bludge?
Remove the rear plug lead see if there is any difference.Yes 95% chance it is the rear one not working.These mowers as you said do run smooth and have little vibration,so if it's rough that could well be a tell tail sign.
