Stay on all the time , even when shut off. New NSS and they stay on when it is disconnected, Cleaned all the grounds, New Bulbs and cleaned sockets, Did a draw test on the battery and the draw goes away when you take the bulb out. What is my next step?????

 

It sounds like someone has wired it in to a switch or something similar. All I can suggest is to look over your wiring and find anything that doesn't look factory, which can be a lot.

Look at the wiring to your reverse lights and take note of its colour. That should be the colour of wire that's been messed with.

 

Brake lights work correctly? Maybe someone got the bulbs in the wrong holes and your brake lights are stuck on? NSS and reverse lights shouldn't have power when the key is off.