Friend has a 2010 FLHTP with no security and his stays on all the time the bike is on.Had that happen once with my 2010 RG w/security the left turn signal also stopped working,ended up being a bad ground.
My FLHP doesn't have security either. When I first bought it (used with 34K, 55,800 now), the light would periodically come on and go off. Now it's on all the time and never goes off. No codes, just a light that stays on. A couple of months ago, my ABS light came on and stayed on. Took it to the stealership to get checked. Said the ABS worked fine, but I had a short in the tach. Wasn't about to spend the $$$$ just to change that. When the tach quits, I'll fix it then. Tracy