While there are no specifically direct references to solar or lunar eclipses in Norse mythology, if we pick through The Poetic Edda, an anonymous collection of old Norse poems, we can find a narrative that supports some of the folkloric rituals that accompany an eclipse.
Through the poems, we learn the sun and moon are personified by the figures of Sol and her brother Mani, two figures that move through the skies each day:
Mundilferi is he who begat the moon,
And fathered the flaming sun;
The round of heaven each day they run,
To tell the time for men.
VAFTHRUTHNISMOL – Stanza 23
Sol is carted through the skies in a chariot, pulled by two horses, specially equipped to withstand the burning heat of the sun:
Arvak and Alsvith up shall drag
Weary the weight of the sun;
But an iron cool have the kindly gods
Of yore set under their yokes.
GRIMNISMOL – Stanza 37
Now if dragging the weight of the blazing sun across the sky each day wasn’t challenging enough, the two horses also had Skoll, one of the children of the great wolf Fenrir, chasing after them, while his sibling, Hati, chased after the moon:
Skoll is the wolf that to Ironwood
Follows the glittering god,
And the son of Hrothvitnir, Hati, awaits
The burning bride of heaven.
GRIMNISMOL – Stanza 39
Now the Norse believed in Ragnarök (the twilight of the gods), a series of battles in which the world as we know it would end; many of the old gods would be fated to die, and the world would be destroyed through a series of cataclysmic events until eventually sinking beneath the waters, only to be born anew. One of the signs of Ragnarök would be that Skoll and Hati would finally catch with both the sun and moon and devour them:
The giantess old in Ironwood sat,
In the east, and bore the brood of Fenrir;
Among these one in monster’s guise
Was soon to steal the sun from the sky.
VOLUSPO – Stanza 40
So, what does this have to do with an eclipse? There are reports of folkloric traditions where people would bang drums or pots and pans during an eclipse to scare away the wolves, which given the mythology, suggests that they believed an eclipse was caused by either Skoll catching Sol in the event of a solar eclipse, or Hati catching Mani during a lunar eclipse. So, regardless of academic arguments over whether this is truly eclipse mythology or not, the fact that rituals have sprung up around it means that for many, there exists belief.
*********************************************************************************

Note: this post used the Henry Adams Bellows translation of The Poetic Edda