try this. Fix the nuetral light issue. you need to study the wire diagram in your manual. Starting at the key you need to inspect, clean and repair or replace, All the switches and connections between there and coils. Sounds like you have a short somewhere. The light issue and the running OK for a while then running bad are most likely seperate BUT maybe connected issues. Hot coils is going to be either bad supply voltage, failing coil windings, or bad plug wires / connectors. Nuetral light could be a bulb failing or any connection or switch in the circut. Dirty run/stop switch itself can cause MOST of your symptoms.
93 VT1100C Harley Killer (1150cc), VH Exhaust, 2mm sleeved and bored, Modified Heads and Valves, Adjustable Timing, Touring Seat, Baby Apes, Metzlers