My money would be on stuck float in the left carb. In my experience, left carbs stick much more than right ones, especially on a cruiser like the Eliminator which doesn't have a centerstand. Leaned over on the side the way they are wreaks havoc on that low carb. Personally, I would send the set off to the dude that services carbs here
As far as the electrical issue, dig into the wiring and start cleaning. Being that your ignition wiring is affected, I would look for rubbing around the headstock and any place where things could get pinched. Somewhere some insulation is getting worn thin, I would think.