Covering The Parrotlet's Cage

I wake up at 7am, go to work at 8am, and I don't get back from work
until about 6pm. I'd like to play with my parrotlet after dinner,
sometime between the hours of 8pm and 11pm or 12pm. This leaves me in a
pickle, since I'm not home during the day to uncover the parrotlet. I
can either uncover the cage at 8am (which means the parrotlet would be
uncovered for more than 12 hours), or I can leave the parrotlet covered
all day until I return home at 6pm. Which is better, and what are the
possible side effects?

How thick does a cage cover need to be to prevent parrotlets from
being exposed to too much daylight (i.e. days longer than 12 hours)?
Does the cage cover need to be heavy to block out all light, or will a
light white bed sheet suffice?

I cannot imagine keeping a bird covered all day unless you were awake with it all night. Keeping a bird in the dark for almost a 24 hour period of time I think would be detrimental to its general health and also be inheritantly cruel. Most people work or go to school all day and spend time with their bird when they arrive home. If you uncover the bird at 7 AM and put it to bed at 7 or even 8, while it would be more than 12 hours, I don't think it would be as harmful to a bird as keeping it covered all day and all night and still allow you a couple of hours of time to spend with it. If that doesn't work with your schedule, I would not get a parrotlet or really any bird for that matter. The only birds I know that can spend all day and all night in darkness are owls.

The birds need darkness that blocks the light shining on the eyes. Anything that keeps out the light would be appropriate. A dark towel or blanket would work.