Some bikes are wired so that if a brake light or tail light or the horn or headlight fails, the ignition cannot work. This is someone's idea of a safety feature.. Or, more likely imo, it is an effort to conform with some local moped classification-laws that demand working tail lights or a horn, etc. Manufacturers need to get government approval before they can sell their bikes.
If that bike runs at all, i wouldnt suspect ignition problems. More likely it is carburation/fuel delivery or driveline troubles.
For instance, if the bike has a belt drive / variator setup, a broken variator will keep it in low gear.
And check out the entire fuel system from the gas tank to the engine block for adequate fuel flow and fuel or air leaks, etc.