Motorcycle Repair: ignition sputtering under acceleration, engine case, electrical problem

Question
Mike,
I got a '91 evo custom bike.  I took it out and it ran fine for about an hour, and then this problem began developing growing worse and worse with time.  As I would take off the line, the ignition would sputter, instead of being smooth.  The lights would dim in unison with the sputtering, (so it made me thin thats its an electrical problem).  It seems that the more aggressive I would be at taking off from the line, the worse the sputtering would get.  If I accelerate slowly, maybe there would be one or two small sputters, but if I really opened it up, the gaps between ignition would grow so large that the engine would risk turning off (also the headlight would flicker in unison with the engine's fits and starts.)  Why did this develop after an hour of riding, while which the engine responded normally?  PS I have this electrical unit (not sure exactly what it is) thats mounted at the bottom of my downtubes infront of the engine.  It has 2 wires plugged into the front of the engine case.  Then its got another wire that goes into my ignition control module.  After inspection, I realized that that wire that leads to the control module is exposed and may be rubbing the frame. Could that be the culprit?  But if it is, then how do you explain that everything ran fine for an hour? And why do the lights also dim in unison with the engine's sputtering?.  And why the sputtering only during strong acceleration.  In a matter of 25 minutes the problem grew worse and worse till the engine sputtered during every acceleration, and would not run smoothly.
Where should I start looking?

Answer
The part you are probably talking about is the regulator. If the wire is rubbing anything, then its shorting the battery which would cause your problem. Durning acceleration it might be vibrating and touching somthing
Good luck and happy riding
Mike