Okay... Celestial objects are gods or remnants thereof, and their interactions have mythic significance.

So what craziness happens if either of the moons, the dead husks of Lorhkan's god-plane, eclipse the sun, the hole torn open into Aetherius when Magnus went "Screw this I'm outta here"?

THe book Heavy armor repair says you should never work on daedric in an eclipse.

One of the daggerfall books makes mention of a mage who was born during an eclipse of Tamriel's moons and thus was extraordinarily gifted.

but honestly, I can't find anything in the Imperial Library that seems particularly relevant to your question.

Not sure. The moons are feeble enough to let star light through, so the solar eclipse could actually cause the moons to vanish. Such an illusion must be significant, but I don't know what it implies.

Is that when the Mane is born?

No, that is when a "third moon appears in the sky," which has been speculated upon a lot.

So Magicka gets interrupted. What would happen during a full dual lunar eclipse?

So magick goes defunct or the lunar lattice disappears, depending on whether the moons block the sun or the sun evaporates the moons - both have potentially catastrophic consequences in worst-case scenario, it would certainly be interesting to theorize the potential variables.