Often, when one finds this epithet of Aphrodite, it is in reference to the many iconographical depictions of her riding a goat. Such depictions seem to appear towards the end of the Classical era and refer to her role as Pandemos, especially in Athens, which Plutarch explains in Theseus, 18:
“When the lot was cast, Theseus took those upon whom it fell from the prytaneium and went to the Delphinium, where he dedicated to Apollo in their behalf his suppliant’s badge. This was a bough from the sacred olive-tree, wreathed with white wool. Having made his vows and prayers, he went down to the sea on the sixth day of the month Munychion, on which day even now the Athenians still send their maidens to the Delphinium to propitiate the god.  And it is reported that the god at Delphi commanded him in an oracle to make Aphrodite his guide, and invite her to attend him on his journey, and that as he sacrificed the usual she-goat to her by the sea-shore, it became a he-goat (‘tragos’) all at once, for which reason the goddess has the surname Epitragia.” (trans. Bernadotte Perrin)
At first glance, it is hard to see how Aphrodite Epitragia relates to Aphrodite Pandemos or even the Aphrodisia. According to Plutarch, Aphrodite Epitragia places herself as Theseus’ personal guide in the journey that would lead him to accomplish the synoikismos (lit. “coming together” of cities) and establish the cult of Aphrodite Pandemos, which is at the heart of the Aphrodisia.
While the depictions of Aphrodite riding a goat appear quite early on in Athenian history, the epithet “epitragia” only appears in later sources, one being the quote cited above from Plutarch, and the other being an inscription on one of the seats in the Theater of Dionysus, also dated from the 2nd century AD, probably the seat reserved for the clergy in charge of Aphrodite’s cult under this epithet.
And this is, honestly, quite curious. If Aphrodite riding a goat was, until the turn of the millennium, mostly an iconographical and artistic depiction referring to her role as Pandemos, it is surprising to see that the cult of Aphrodite Epitragia had a clergy, as attested by the presence of the seat in the theater, and it mostly raises the question of the purpose of the cult. Was it different from the cult of Aphrodite Pandemos? If that was the case, how so? Was the cult of Aphrodite Epitragia always there despite the fact we have no trace of it before the 2nd century AD? etc.
In L’Aphrodite grecque, V. Pirenne-Delforge interprets Epitragia as a guide in the sexual coming of age of Theseus. In the same manner that another legend associates the cult of Aphrodite Pandemos as a patron the sexuality of young people through the opening of a brothel under Solon (6th century BC), the Thesean version would represent Aphrodite foreshadowing the metamorphosis of Theseus from a child to a man with the miraculous change from a she-goat to a he-goat. V. Pirenne-Delforge also points out that the image of Aphrodite riding a goat is not exclusively used to refer to Pandemos, as it is the case on ex-votos where she is represented in her Ourania aspects as well.
Still according to the same author, both the epithet and the iconographical trope seem to have been more akin to a protection than an actual representation of the goddess, popularized by the sculpture of Scopas in Elis, which represented Aphrodite in this manner (unfortunately lost to us). This conclusion can only be reevaluated if we find depictions of Aphrodite Epitragia that were made before the 4th century BC.
Vinciane Pirenne-Delforge, L’ Aphrodite grecque. Contribution a l’etude de ses cultes et de sa personnalite dans le pantheon archaique et classique, Kernos, 1994.