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Question: What was the appearance of Amaterasu when she was hiding in the Rock-Cave of Heaven?
Answer: Since Amaterasu is the sun deity, she had the appearance of the sun-disc. Another tradition says: When Amaterasu retired into the Rock-Cave of Heaven after her descent from Heaven (sic), she took on the appearance of a dragon-fox (shinko). Uniquely among all animals, the dragon-fox is a kami that emits light from its body; this is the reason why she took on this appearance.
Question: Why does the dragon-fox emit light?
Answer: The dragon-fox is an expedient body of Nyoirin Kannon. It takes the wish-fulfilling gem as its body, and is therefore called King Cintāmaṇi. ... Further, one tradition says that one becomes a king by revering the dragon-fox because the dragon-fox is an expedient body of Amaterasu.
Commenting on the sokui kanjō, Bernard Faure writes:
under the name "Fox King," Dakiniten became a manifestation of the sun goddess Amaterasu, with whom the new emperor united during the enthronement ritual. [...] The Buddhist ritual allowed the ruler to symbolically cross over the limits separating the human and animal realms to harness the wild and properly superhuman energy of the "infrahuman" world, so as to gain full control of the human sphere.