I cover the top, three sides and 1/3 of the front of my cages at night and use a night light in the room.
Covering the cage at night helps the budgie feel more secure while darkening the atmosphere to encourage it to sleep. A night light is used to give the bird enough light to see which helps prevent night-frights.
I throw a twin sheet over my cages. My budgies truthful are very laid back and roll with the punches. I cover both cages more for the sake of my neurotic but lovable cockatiel who will start screaming in the middle of the night if I don't.
I have two cats that like to do their cat business at night and are active. I cover my budgie cage so my two bebes aren't woken/frightened constantly throughout the night from my cats just being cats.
Also I can't make them sleep once they are covered, but I find that they usually go to sleep within 15 minutes of covering and this way I can help to ensure no eggs by limiting their waking hours.
Do not use towels or material that has an open weave that tiny claws can become stuck in, also budgies love to nibble and ingesting fibres is definitely not good for them. I cover my cages also. I leave the covers on the top and a little down the sides especially if the cage is near a window. Predator birds have tried to attack my cages through the window, this can cause a fright and a budgie could take flight or become stressed. I cover the cages and provide night lights as well. Only last night I had one of my birds flapping around because his cage mate thought he should not be sleeping where he was. With the light he could then climb back up, budgies do not have good night vision at all.