My back brake lights stay on my 2005 road king classic.

That will be either the front or rear switch sticking, first try unpluging the front brake light switch, with this disconected if the light stays on the problem is with the rear switch, locate the switch this will be close to the brake pedal normal spring opperated which can stick, check it is closing fully, you may also disconnect the switch and check the light goes out reconnect the front switch and check correct opperation, this would thenpoint the fault towards the rear switch