New switch is shot

A bit hard to follow. Sounds like you installed a new ignition switch and think that is the reason your starter latched on. More likely, you have a connection in the wiring runs between the IGN1 (green) and Start (yellow) wires. One strong suspicion would be in the bulkhead connector, especially since you lose spark erratically and your lights flicker. Many, many posts on this. Your starter relay could also be bad.