Can this [Greco-Roman] myth [of Echo and Narcissus] be the source of the rabbinic bat-kol? It certainly is possible; other Greek myths show up in rabbinic literature in concealed form, too. And because an echo has no clear source and seems to come now from nowhere in particular, bat-kol took on its second meaning of “a voice from the blue” — that is, a heavenly pronouncement. A bat-kol, for the early rabbis, was not the same as the voice of God that was heard by the biblical Prophets and did not have the weight of prophetic authority. Its status, indeed, was ambiguous, since the hearer of it could never be sure just where it emanated from or whose will it reflected. Heaven, in rabbinic thought, was also populated by angels sometimes acting on their own, and a bat-kol could come from them, too.This reminds me a bit of the old joke about the man who fell off the side of a high cliff but managed to grab a bush a partway down. He called out, "Is anyone up there?" Then a voice from heaven thundered, "I am here. Let go of the bush and I will catch you." The man looked up at heaven, looked down at the ground far below, and then looked up again and called out, "Is anyone else up there?"
The bat qol (bat kol) figures in earlier PaleoJudaica posts here and here.