You’ll have an after market starter solenoid, i have two bikes that do this. Haven’t bothered to work out how to wire them so it doesn’t do it properly yet, but soon as i do i’ll let you know.
Others have dealt with this issue too, i am sure they’ll chip in shortly.
Because of the new starter relay, 2 of the connections are reversed (It doesn’t matter in practice as they are for the main fuse, i’d expect.) there’s a diode in the loom to prevent power looping back from the starter circuit to the neutral light.
When you pull the clutch in, normally it would circuit to earth, but isn’t. See the silicon rectifier in the middle of the diagram? That’s now running in reverse. I’d say if it’s reversed again the issue will go away. Either that or i’ll look how the starter solenoid connector needs to be wired differently to it to remove this happening.
More than likely the 2 connections across the fuse simply need to be reversed. I’m going to buzz it out with a meter before i recommend you do so though!