Try turning key on, try engaging reverse lever again (may require you to slightly rock bike back and forth to get it into position, LEVER UP) then, take it our of reverse and see if the light goes off. If it won't fully go into up position DON'T FORCE IT!!!
I am assuming as you said lever IS NOT up, and bike won't start. This is a safety precaution as starter button is your reverse.
Happened to me one time when mechanic forced the bike into reverse and. You have to let it go in by itself, sometimes requires this slight forward/back rocking while engaging. Sounds like the engagement rod may have gotten stuck. If so you probably have to take it apart, get it loose, line it up properly and lube.
2012 Black XC Tour, HELI bars,
1.5" lowering kit, Closeup Seat, Heli bars, Reverse, "sans cats", ATS, IAV, PC5, m.o.u.s.e...
2nd in command... 2016 Honda NM4