Hello, the neutral indicator wire seems to have a current when the bike is not in neutral but doesn’t when the bike is is neutral but the light on the dashboard works as it should. Why is this? 

I'm electrical challenged at the best of times but at this stage I can only think go through all the wiring in the headlight bucket & take very close note of color matching. Example being there's light brown battery power after the switch & there's dark brown & dark green which is flashers left & right from the flasher handlebar switch. Only mentioning those colors as can get a bit confusing. Probably nothing to do with your current problem though.

As I understand it (but not guaranteed to be correct!), bulb terminals are Sky Blue and Brown. Brown is "switched" live - ie power goes to it when ignition is on. The Sky Blue is effectively the negative terminal and is activated when neutral is engaged, presumably by one of its parts contacting the engine, which should be in direct contact with the frame (ie not insulated by thick powder coat paint on frame!).

called a low side switch

grounded when current flows

main switch is high side +
completed circuit is when grounded -

2 switches turn it on.......key/main switch AND ground switch or neutral switch

You say dashboard lights work as they should. Do you mean the ones illuminating speedo & tachometer as they're AC powered when engine us running. Sorry might have to eat my words there if you have an electric start 125, I can't remember where this started haha in which case everything is DC powered. Ignore me best way. Have a good day.