If your bird squawks and fusses in his cage, covering the cage routinely may help him calm down. Even a captive bird who doesn't initially like his cage covered may develop a strong preference for it -- so much so that he squawks as a way of telling you to cover him up. His appreciation for being covered will stem from a variety of emotional needs more easily satisfied when the cage goes dark.
Fear of Outside
Caged birds can feel vulnerable, especially when they are startled by things they don't understand. For example, placing your bird's cage near an open window can terrify him as people, animals and car headlights appear outside the window. Even if his cage isn't near the window, the constant leering of a curious dog or cat can unnerve your bird at night and make him squawk. Covering his cage at night prevents him from seeing these frightful distractions, making him feel safer and less anxious.
Need for Sleep
Birds need to get their beauty sleep. If they don't, they can become anxious, irritable and vocal. Even birds who aren't frightened by what's outside the cage can become distracted, interrupting the sleep schedule. Covering the cage is like turning out the lights -- it gives him what he needs to be able to get a good night's rest without interruptions.
Love of Routine
Just like dogs and cats, pet birds thrive on a consistent routine and prefer predictability in their day-to-day lives. Covering the cage at night is your way of signaling to it's birdie bedtime. Do it at the same time daily to give birds a sense of schedule. Without that reliable structure, captive birds can become nervous and stressed, which they express by squawking. His vocalizations may be his way of telling you he's waiting to be covered up, because that's become part of his routine.
Avoiding Night Frights
Even if your bird prefers to be covered at night, he may fall victim to night frights. These occur when your bird is suddenly awoken at night by something such as a light or a sudden noise. When the cage is covered, he awakens disoriented and, in total darkness, may squawk and thrash in his cage. He may hurt himself in the process. When you cover his cage, leave a night light on in the room and run a "white noise" machine quietly for ambient light and sound. This prevents the sensory deprivation that can frighten a covered bird who unexpectedly awakens at night.