Like Rerun said, you don't have mechanical points on a twin cam. Your have a pulser ( on the end of the crank) that feeds the signal to fire to the coils. You also have spark units, which are basically little CDI boxes to help boost the spark energy.
Inside the pulser is a magnetic switch that operates like a set of points. When the tip of the ignition rotor passes by the pulser it causes the magnetic switch to close, and that is what triggers to coil to fire.
The only thing I could imagine is a stuck pulser, and that would be a pretty odd thing. There's an air gap clearance that needs to be set, but an improper air gap would lead to no, irregular or weak spark. It can't really lead to a continuous spark, but the FSM will show you where to set the air gap to rule out that possibility.
It may be possible the one of the spark units ( CDI's) is faulty, but as I dont fully understand how they operate I cant even begin to diagnose that part of the system. The FSM might be your friend there.
Good luck, and let us know what you find. This is interesting.