There was this image that was popularized in the media back in the 30s and 40s of an actor, lounging between takes, sitting in a director’s chair, wearing sunglasses and a robe, and smoking a cigarette in a long black holder.
Note also the starter’s pistol in Cecil B. DeMille’s right pocket. He would use it to get a reaction from his actors when needed — or just to get order on the set!
Sitting on a director’s chair. In the early days of movies, that was the folding chair. It was easy to move, and is still probably the most comfortable portable chair around and when shooting on a number of different sets, and having to sit and wait for your scene, portable and comfort are important.
Lounging in a robe. A couple of reasons for this, costume people don’t like you getting their costumes wrinkled and speckled in food and make up or anything else so they demand you wear something for cover or to take it off and hang it up. Continuity people also get upset if new spots appear on your clothes between scenes. So generally, if you are a featured player, your costume is hanging up in your dressing room/trailer and you want to be covered without getting overly dressed which means a robe.
Smoking with a long cigarette holder. Back in the golden age of movies, everybody smoked, and if you were wearing the early makeup, it was, depending on who you talk to, easly melted or even flammable so you wanted to keep the cigarette as far away from the makeup as possible.
The sunglasses. Studio lights are still killers and in the early days of film were especially bad. Add to that that actors and actresses do not want to develop squint lines in earlier than they have to, they wear shades as much as possible.
No cite, I am afraid, basically from experience and visiting with people in the business.