Cozcacuauhtli's patron is Itzpapalotl, the obsidian butterfly, a fearsome goddess associated with the Tzitzimime star demons and with the Chichimec peoples of the northern deserts, a considerably more severe patron than the vulture sign's own gentle, patient augury might suggest, one of several cases in the count where a day sign's reading and its governing deity's usual character do not obviously match, the assignment recorded in the sources without an explanation connecting them. Its direction is south, the fourth instance of that direction after Cuetzpalin, Tochtli and Malinalli, standing at the recurring interval the rotation follows.
Cozcacuauhtli is not a year bearer, sitting between Acatl at thirteen and Tecpatl at eighteen, outside the select spacing. Itzpapalotl's patronage of Cozcacuauhtli as a day sign is a separate office from her role as trecena patron of Trecena 15, opening on Calli the house sign, where her severity governs a difficult week far more visibly than it does here, so the obsidian butterfly's harsher character finds fuller expression in her trecena patronage than in her comparatively muted presence behind the vulture's gentle day sign reading. Itzpapalotl's association with the Tzitzimime, the star demons feared most during a solar eclipse, connects her severe reputation to Mexica anxieties about the sun's own survival, an anxiety the vulture sign's patient, unhurried reading sits at a considerable emotional distance from despite sharing the same governing goddess.