Ugh... so many questions... (drum roll please) it is a 2000 ZG 1000 (C10) and it has 11,000 miles.
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Low miles, 17 years old. My money is on the carb(s).
FWIW, and YMMV, the ignition system is fairly bullet proof. If a component in the ignition system fails, it'll typically affect two cylinders. Sparkler plugs the exception.
You could dry a double/triple dose of "Tune Up in a Can". Run the bike low on fuel, add the "Tune Up in a Can" and start the engine for a few minutes. Let it sit for an hour or two, then *ride* the bike til almost out of gas. Approx 50 miles once you hit reserve. Refill the tank and burn out the remaining "Tune Up in a Can" on your way home.
If that doesn't work, pull the carbs (a major chore) and clean them on the bench. Bubba, I mean Steve in Sunny FL, does this as a service. He's quite good. *Your* issues will be removing the carbs and reinstalling them again. The rubber boots between the airbox and carb inlets will be quite stiff and hard, you may need a third hand too. Often warm air from a hair dryer will help soften them up at the install stage.
Rick