Hi I'm new to this form. I have a 2005 Deuce and my break light stays on. I've unplugged the switch and it is still on. Any ideas as to what the problem might be

 

Welcome to the Forum from Colorado!
Sounds like the switch up at the hand brake lever has fallen out of place or is broken.

 

There are two brake light switches on your bike. One for each front and rear. If you unplug them both, and the light still stays on then you have a short to ground somewhere. If the light goes out then one, or both are bad. I would also check the front brake light switch first. These are easily damaged if you try to remove the right controls without spacing the brake lever.