the actual neutral sensor would be my guess - could be the sensor or could be a bad connection somewhere - i'd recommend taking all the connections off (one at a time) then clean em and put em back together with dielectric grease (keeps water out and corrosion away)

 

I could see that coming in handy in certain situations on the trails.

 

The sensor is down by the front sprocket in the side of the engine case.
Yes they will start in gear.I had my bike against a tree in my front yard while doing maintenance and a few cold ones and hit the start button and fired her right off the tree with a nice kerplunk of falling right onto it's side after it cleared the tree...LOL it's the only time i ever did it....

 

my old ninja had that switch broke and watched it launch off the kickstand a couple of times[&:]

 

i was having problems with the light even before i bypassed the switches (kick start, and clutch) its came on today for a little bit, but i think that your right, the connection is probably full of water and mud (as it should be) so i think its due for a good scraping/cleaning/greasing... i'll be sure to let you know if it fixes the problem.

 

Pull the wire off the actuator which is down near the front sprocket.
Touch this wire to earth (any metal part of the engine or frame)
if the neutral light comes on when this wire is grounded then the actuator is faulty.

This only takes a second to do.