By the schedule you have your bird on you are messing with his natural cycle. Birds roost at dusk and awake around dawn so he will wake up as soon as it starts to get light covered or not. I would say your bird is more than likely not getting enough sleep. I'm no expert though so hopefully someone with a better grasp of this will comment as well.
This is true to an extent (but I do think it's more about consistency of bed-time/wake-up and indoor lighting adjustments). I say this because in the USA, there is no way for me to keep my bird up until dusk and wake her up at dawn, as the light cycles near the equator that dominate my bird's sleep needs/instincts are totally different here. Near the equator, there are 12 hours of light and 12 hours of dark year-round. If I put my bird to bed at dusk, she would be up until 9PM then she would be waking up at 6AM again (with the sun).. 9 hours would NOT be enough sleep. That having been said, OP's bird probably isn't sleeping enough, as that schedule is pretty far from what would be normal in terms of lighting etc. You want to get as close to natural as possible without keeping them up too late.
Is the Sun always up for exactly 12 hours at the equator? (Beginner) - Curious About Astronomy? Ask an Astronomer
I also think that by covering your cage (when your bird is still awake in there for 2 hours after, from 9-11) could also lead to other issues.
If I were you, I would look into getting a sleep cage so that your bird can be in its own quiet room during night-time hours. If you cover at 9, your bird should fall asleep within an hour max. We are talking beak grinding etc within 20 minutes. If that isn't happening, something is off (too loud, not ready for bed etc). They have very good internal clocks and the sleep needs to be consistent. If you put the bird to bed at 9 (in a dark quiet room) then it should actually go to sleep then, but that also means you need to be up at 9 to get the bird uncovered (even if it means setting an alarm). It isn't good for them to be covered and awake for too long.
If a bird is covered but it still is convinced it needs to be up (so much so that it moves around for 2 hours in the dark), it can lead to weird hormonal issues. If this is happening in the morning and the evening, that will further compound the issue.