The V2 only has one headlight so they don't seem to suffer form the loads on the start switch.
The neutral light and the gear position indicator could be reading differently that is why I suggested looking at the position indicator.
The priming of the fuel pump is the most important part.
If you don't get the prime it is most likely one of the safety switches like kill switch or the kick stand switch (only if the bike thinks it's in gear)
If you get the prime the clutch switch could be a suspect, it's a easy test so a good place to start.
Some of the 19 rides in my shed
2014 V2, Snoopy
2009 Wee, Pumbaa the pig
WR450F, The Blue Postie Bike
YZ250N smoker with rego, Stinky.
Yamaha MT09 (FZ09), The Scud missile.
Club Lead not Club Med.
He with the most toys wins.
Out of my depth in a puddle.
Live life on the edge you will see more that way.
Ridding a motorcycle keeps things in balance.
At the end of each trail and at the end of each day history is made.