I would leave to closet doors open as much as possible for air flow. The air will get stagnant in a small closed space, will likely remain too humid, stinky and just not be a healthy environment. They should have somewhat of a day/night cycle but it doesn't have to be bright light. I kept my crested geckos in a pretty dark room for years, but a small amount of light did get in around the heavy curtains I used to keep out the heat (and also some ambient light from other rooms). It was enough to regulate their day/night cycles even though it was never anywhere close to full daylight in the room. My collection is now in a different location, in a room that does receive full sunlight as heat is not so much of an issue. I find that their behavior and activity is pretty similar to the when they were in the darker room.