@Poseidon,
Well, we're talking about zillions of galaxies worth of red light. If you see a candle at a distance during the day, you can hardly see it. In darkness it can be seen at quite a distance. There is no other light to overpower the redness.
These are solar eclipses on cloudy days.
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Ben and Alice: March 2006
As you can see from these photos, my memory serves me well. The cloudiness is quite distinct too. I remember being very dissapointed that the one chance I had to see the solar eclipse, had to happen on a cloudy day. But I looked anyway, hoping for a gap in the clouds, and it seems it was a blessing in disguise.
Now surely, considering these pictures, this would have nothing to do with the alleged sunset effect/rayleigh scattering?
Also note that the Doppler effect is well documented, and there is evidently enough red light from the distant galaxies for them to be seen as such.
In the absence of the sun's light, that red seems to shine through enough. Perhaps together with red dwarfs? I still think though, that the dwarfs probably only account for about 10% at most. Just a guess.
But the question which asked
'why is the sky not red during a solar eclipse?' was spot on. Without an eclipse, on a cloudy day, the sky is not blue, even from space. But it seems the red light is then strong enough to be observed when the Sun's light is even partially cut off by the moon, and the blue light is filtered out by the clouds.
We are talking about countless galaxies spewing red light at us, which has been doing so for billions of years, so its accumulated effect is still quite awesome. Some of that light must have left its original source at the dawn of the universe.