A full lunar cycle, from full moon to lunar eclipse could take something in the range of 15-30 in-game days. When a server is started it could be put at a random point in the lunar cycle. At full moon, you'll be able to see much more clearly once it is fully dark compared to normal nights, and on Lunar Eclipse it is all pitch black. In-between days would have differing light levels depending on how close it is to the next full moon or lunar eclipse.
A solar eclipse could either have a rare chance to occur or it would trigger as the result of some event or something. During a solar eclipse, the day will be incredibly dark, almost as if it were night. The length of the solar eclipse is up for debate, but perhaps it could last that entire day since it probably won't trigger very often.