I don't know the failure stats on pulsar coils, but I suspect they are very low. Unless it has physical damage or shows a short or open on the windings, I'd bet it's AOK. Why do you think the ignition coil is OK? Have you made primary and secondary tests on that?
I believe the neutral start just disables the starter from turning, and has no effect on spark. When you say you "bypassed" the safety switch, does that mean you jumpered it or disconnected it? On many, the safety switch is just a grounding switch to disable the ignition, which means if you jumper it you are disabling the ignition. Just disconnecting it would be the way to isolate it as a cause. Not exactly sure if that applies to that particular motor, but something to consider.