The tailgate actually is part of the structure of the bed. Without the tailgate the sides of the bed will begin to spread apart due to road shocks and vibration. So it is important to keep the tailgate in place and up when on the road.
Like others have indicated, keep the tailgate on and locked in place when towing.
When Empty-
It's been proven in tests a tailgate up provides better fuel mileage than keeping the tailgate down. With the tailgate up a bubble of air is created which helps the air to flow smoother over the truck.
Enjoy the 5th wheel.