Theophanies of the Ancients

...of the lights, and then of those that are formed? original Greek: τῶν φωτῶν, τότὲ δὲ τυπωμένων (tōn phōtōn, tote de typōmenōn) How do the manifestations of the present Gods occur—sometimes as lights entirely devoid of form, and sometimes as those who have assumed a particular shape? And he immediately adds: Since the Gods appear at different times in various figures, it is a mystery how, without the divine nature being harmed, it can be seen in various forms. original Greek: τῶν Θεῶν ἐν σχήμασιν ἄλλοτε ἄλλοις φανταζομένων... (tōn Theōn en schēmasin allote allois phantazomenōn...) This doubt he solves in the following way: while the Gods remain immutable and without any diminution or loss of their essence, they assume divine simulacra Likenesses or phantom-like forms that represent a deity without containing their actual essence. which are seen only by those whose minds have first been illuminated by divine lights. Consequently, even though the Gods are incorporeal by nature, they nevertheless put on bodies for our sake, which
Iamblichus, On the Mysteries

Book 2, chapters 10 and 11.

both become manifest and become invisible according to the will of the Gods; original Greek: καὶ φαίνεται, καὶ ἀφανῆ γίγνεται κατὰ τὴν βούλησιν τῶν Θεῶν (kai phainetai, kai aphanē gignetai kata tēn boulēsin tōn Theōn) meanwhile, the Gods themselves remain as they are—inconspicuous. That is to say, they derive nothing into themselves from those temporary bodies or images they have assumed, nor are they changed by them in any other way.
Ibid. Book 2, chapter 10.

Finally, he concludes with this Epiphonema A finishing touch or summary exclamation.: Every God is therefore formless, even if he is seen present in a form. For the form is not in him, but proceeds from him; because the observer is unable to see the formless being without a form, he instead views him through a form according to his own human nature. original Greek: Πᾶς οὖν θεὸς ἀμόρφωτος... (Pas oun theos amorphōtos...)

Thesis 5.

Truly, it was not yet enough that the Gods—being incorporeal in and of themselves—had assumed bodies; but there was also required...