Our lights go on when the awing lights are turned on. The only way to make sure their is no power drain is to put a disconnect off the battery. Otherwise you will have hidden drain, radio, propane leak sensors etc, which will kill your battery in short order.
Others with your model will be able to give you more help on the stair lights.
Good Luck and congratulations on your new RV
2011 Toyota Tundra double cab