Of course, being able to support liquid water does NOT mean there is liquid water and having liquid water does NOT mean there life as we know it.
Actually, outside of the habitable zone there can be subsurface liquid water and perhaps then life as we know it. It is likely that Jupiter's Galilean moon Europa has subsurface liquid water, and so may have life as we know it---but people seem to keep finding reasons to rule that out.
If such a moon orbited nearly in the planet's orbital plane (which seems likely given the ordinary nebular hypothesis), it could have daily eclipses of the parent star. Thus, the near-side of the moon could have an ordinary night and an eclipse "night" every day.
In any case, the everyday celestial spectacle on the moon would be quite different from that of the Earth.