You guys definately don't care about this...but since I am the champion of things that no one cares about...
I Will chime in. But first let me say best regards and luck with your new clan...now to the
Awkward stuff..
Equilux is the word you are thinking about. When there are exactly 12 hours between Sunrise & Sunset. When Night and Day are equal.
Equinox happens at a similar time usually, twice a year, usually only a few days from the Equilux, but its not technically that definition. Though it's kinda fuzzy why not, and its a tad bit redundant but...
An Equinox is when the Northern and Southern Hemispheres have an Equal Nox, or equal night...it has to do with the axis of the Earth...It is defined as the instantaneous event at which the axis of Earth's rotation and the line joining the Earth and sun is exactly perpendicular. So equal divides of nox, or night on the earth.
So your two clans can have a balanced night between you with the name of Equinox, but that name isn't really to do with daytime, its just a very common misconception. That said, yer clan could be called EquiMuffin, as long as you have fun and treat each other right, who really cares?
You have just been Tea'd with useless information. Please cherish this moment, and hold it close to you.

Teaweasel 121 Druid (Morrigan, Clan: Avalon,
On Hiatus)
Teaweasel 133 Druid (Arawn, Retired)
Best Build is a 30/30 in Thinking for yerself
