2001 GZ250 neutral light does not turn on
 

I just recently bought my first motorcycle; a 2001 gz250 with almost 6k miles and it runs amazing! However, i did notice that the neutral indicator light does not work. I understand that i don't need it, but as a new rider it helps me to know i am in neutral without having to guess and feel it out with the clutch. I replaced the bulb, i checked all fuses, i also noticed current is flowing thru both wires that connect to the neutral light bulb. Does this mean the wiring is the problem or perhaps the neutral indicator switch? HELP!