Yes it sounds like a sensor problem...try taking out your reverse and neutral sensor switches and swapping them. The two sensors are both the same part and will interchange, they are located down low on the clutch side of the engine, their is a small defector covering the wiring plug that goes to them, the sensors sort of look like miniature sparkplugs. They have a 14mm head, you will need to either drain the oil or turn the bike on its side because oil will pour out when you remove the sensors. You know that the reverse sensor works as it should already, so if you swap them and your neutral light works but your reverse light doesnt, that will tell you that you have a faulty sensor
Machines owned:
85' atc250r (sold)
85' 250sx- the daily rider
85' 250sx- building w/ fourtrax 300 engine
83' Alt125- the Beast
85' atc70
83' atc70
01' yamaha wolverine 350 yz blue(only bike i ever bought new)
SILLY RIDER! TRX IS FOR KIDS!!!