A bit tangential, but here we go.
A place where there's daytime all the time, except every once in a while is quite close to us. It's the Moon.
If you live on the near side of the Moon, then you always see the Earth hanging there in the sky in the same spot every day. It does not rise and it does not set, it just stays in place. But it goes through phases. New Earth, Crescent Earth, Half Earth, etc.
The Sun does rise and set. A "day" on the moon is half a month long. When the Sun is in the sky, the Earth is at most in "half Earth" phase. When it's nighttime though, the Earth is at least "half Earth".
And seen from the Moon, the Earth is big. Very big. Just take the Andromeda in the picture, and make it a disk. That's how big. (Actually about 15% bigger).
The Earth is also bright. Much brighter than we see the Moon on a bright night. Earth's albedo is about 3 times higher than Moon's. All in all, at "full Earth", you would receive about 40 times more light that we get here from the Moon when it's full.
In other words, when the Sun is not in the sky, you get enough light from the Earth to see around. The closer to "midnight" the more light you get, because the Earth is closer to "full Earth" phase.
Of course, when you have a solar eclipse, you stop seeing light from either the Sun or the Earth. Here on Earth, solar eclipses are quite short. The moment of full eclipse is fleeting, generally it's 3 minutes or less. On the Moon, because the Earth is so much bigger in the sky, the eclipse is long. Of course, we knew that from here: when it's a solar eclipse on the Moon, it's a lunar eclipse on Earth, and that takes hours.
It's not completely dark on the Moon when there's a solar eclipse.
It's not completely dark here either. Because of the Sun's corona. The apparent diameter of the sun is virtually identical with the diameter of the Moon as seen from the Earth, but the Sun's corona extends a bit further, so we get to see it during total eclipse.
But on the Moon, the Earth is so large that the Sun and the corona are fully obscured during total solar eclipse. What you will see instead is the Earth atmosphere. Very thin, impossibly thin, you will not be able to perceive its thikness. It will just look like a one-dimensional line. A part of it will be very, very bright. And very red. It will be a very bright, very large and very red circle in the sky.
You will also see the inner planets, Mercury and Venus. Normally you can't see them on the Moon, but during a full solar eclipse they'll be quite close to that bright circle, and they'll be very bright themselves.
And what a glory the Milky Way will be at that time. And if you are lucky, you'll see that very oblong shape that's the Andromeda. Somewhat faint, but still, much brighter than any of us here on Earth would perceive it.