Green light neutral problem with Honda rancher

I have 2006 400 Honda rancher with manual or automatic shifting.

Problem is my Honda only starts in neutral and only when green neutral light is displayed.  When shifting into neutral, sometimes the green neutral light will not display.  When this happens, atv will not start.  If I jiggel the forward /reverse/neutral shift gear stick the green neutral light will come on and i can then start the honda.  The green neutral light is becoming more and more difficult to get to come on.  I feel i will be out ice fishing and not be able to restart the honda.  Has any one else had this problem and have they found a remedy

Thanks for any reply.  Shellfish

Sorry,  forgot to name the shop.

Auvinen Service center.  Ironwood michigan

Found a small fix it shop in Ironwood U.P.  I feared the worse and the best resulted.  Turns out my shift linkage was corroded and gunky from road salt.  They cleaned up the shifting system and behold it shifts like butter and drops right into neutral with the green neutral light always activating.  This allows machine to start.  40.00 dollars

When's the last time you got a deal like that at a small fix it shop.  Or any place.  Very nice folks.  They are a honda dealer.  Guess thats why they have 5 star rating.

Are you shutting the engine off when it is still in gear?  I have an older rancher that is sometimes hard to get into neutral when the engine isn’t running so i just make sure I shift before i shut the engine off.

Might be the neutral switch, do a internet search and see if anything matches your machine