OK, let's review:
a) Is he in complete darkness when you come in or are there lights coming in from the street or other rooms or a corridor or whatever? People who live in cities don't actually experience the same dark of night as in the country or the jungle but they don't even realize it because they are so used to living with a certain amount of light.
b) Is he fully exposed to the sunset every single day? People usually have a routine that doesn't really take into consideration the changing of the seasons. If you and your wife sit down to watch TV every night after dinner, say at 7 or 8 pm, it would be day during the summer but complete night during the winter. It makes no difference to us but it makes a difference to birds. Also, if his cage is not in front of a window or the window shades or curtains or whatever are not completely open, he would not get the full benefit of the twilight.
c) Can he see the TV from his cage? Because they have found that the way TV emits light to form the pictures on the screen (with super fast flashes) creates the same brain wave lengths (alpha) as those of people who have Attention Deficit Disorder and makes children hyperactive. I have since started advising everybody not to expose birds to TV and to leave a radio on if they want the bird to hear human voices when they are not there.
d) Is it possible that he is fast asleep and you wake him up when you walk into the room and cover him with the cloth? Some small species (tiels are famous for them) are prone to night frights when startled out of a deep sleep.
e) Why cover him if he is already in darkness? Does somebody in your household get up before dawn to uncover him so he is exposed to the sunrise? Because they need dawn to start the 'clock' and dusk to stop it and the time in between is what makes the difference (point of refractoriness).
Complicated, isn't it? And people get birds because they think they are low maintenance and easy to take care of
