When the neutral light coming on while riding and especially if you ride in the rain, the neutral switch on the trans top cover is what I suspect doing this. I replaced 3 of them on my 07 RK and after the third one, I installed the frog mouth cover to protect it from water infiltration and that ended the problem for me.
If by chance this light comes on again while riding, pull over and shut the ignition off then back on and try to start the motor in gear with the clutch handle out (hand not on it).
Just tap the start button to see if the bike lurches. If it does lurch being it is in gear, change the neutral switch.
When the switch goes bad this is the quick and easy way to test that. The circuit in the neutral switch handles both the neutral light and the clutch safety switch so the lurching of the bike confirms that a circuit is operating incorrectly in the switch, the engine should not crank unless the clutch lever is pulled in. The switch has two functions as stated above and this applies to 07 and later bikes.
There's a new switch available with an improved "O" ring seal to keep the water from infiltrating the switch.
Take a look here...
False Neutral Light On - Harley Davidson Community
If by chance this light comes on again while riding, pull over and shut the ignition off then back on and try to start the motor in gear with the clutch handle out (hand not on it).
Just tap the start button to see if the bike lurches. If it does lurch being it is in gear, change the neutral switch.
When the switch goes bad this is the quick and easy way to test that. The circuit in the neutral switch handles both the neutral light and the clutch safety switch so the lurching of the bike confirms that a circuit is operating incorrectly in the switch, the engine should not crank unless the clutch lever is pulled in. The switch has two functions as stated above and this applies to 07 and later bikes.
There's a new switch available with an improved "O" ring seal to keep the water from infiltrating the switch.
Take a look here...
False Neutral Light On - Harley Davidson Community