1/ So here's the interpretation of the riddle. While short, it combines many elements present in European mythology. The moon, as we know, directly affects Nature and its cycles are closely tied to women. The moon is also a mirror, in the sense it reflects the light of the Sun... https://twitter.com/Herminius_Mons/status/1262472134665920514
2/ The myth itself mentions the mirror. The "dreadful" wailing woman drawing the moon to the underworld is a parallel with the banshee, an old woman whose scream announces death. The wailing could also signify the newborn as you can see in this thread: https://twitter.com/LHwicce/status/1258676828383973376
3/ The river Styx is the mythological river leading to the underworld, showing a degree of Greco-Romanisation in Iberians. Let us return to the moon. @AzcurrainMaria made an excellent thread on its symbolism among Basques so I'll use it as inspiration https://twitter.com/AzcurrainMaria/status/1258507050717339650
4/ In Basque, the moon is called ilargi. As Eguzkilore presented in her thread, it has the ultimate meaning of "Light-lady of the dead". The woman, tied to the moon, is the nourishing mother, and through which our ancestors are reborn by creating new life.
5/ The moon, as a mirror of the Sun, is in a way a reflection of yourself in your new life, beget by your mother. And the cave, of course, is a symbol of the womb. With all the pieces of the puzzle available, we can now put it together...
6/ The moon during the eclipse is shaded. It represents the end of YOUR life. The wailing woman, the "Light-lady of dead", announces your death, guiding you through the underworld to allow your rebirth. You pass as a mortal, but you will soon return to immortality through rebirth
7/ The wailing is a symbol of your rebirth, when you exit the womb of the mother you scream, as you come back to life and start, once more, the initiation rituals of rebirth. The Iberians, during the eclipse, would simulate the loud noises of a newborn baby, as Sisibut tells us
8/ I also suggest you read this thread on the significance of the mirror. You will see the ties with rebirth and the moon even more clearly. And, of course, you also have the Snow White fairy tale, dealing with the same themes of rebirth and the mirror... https://twitter.com/KomninosM/status/1247142269360226304
9/ The riddle was no superstition to try to explain the origin of eclipses as the King thought. It was merely the observance of a pattern in Nature related to our own rebirth process. Of course, being clouded by Christianity, Sisibut could not see its meaning. Thanks for reading!