What year is the bike? How old is the battery? Do you keep it on a trickle charger?
You’re right, if it’s cranking then it’s not the neutral switch. Does it crank at full speed with the clutch out? It might be battery related as Natrix suggests, with one sensor parameter out of limit for the ECU, that comes into range with the marginally lower drag of pulling the clutch in.
Try disconnecting the clutch switch, and see if the problem is linked to the mechanical action of disengaging the clutch, or to the action of making/braking the electrical circuit with the switch.