E.g. the god Chronos. Do the actions of Chronos reflect the thinking about time held by the author, and was there a conscious attempt to channel the author's idea of what time is to the people?
The founding of these religions are too old to know. You might start with Hesiod's Theogony, but that text--like most that treat myth--are descriptive of contemporary practice. That is, they aren't actively engaged in creating myth (or what's called mythopoesis). By contrast, Tolkien creates myth in his Silmarillion.
If you look at a text such as the Aeneid, Virgil is working within established traditions. So he isn't creating mythology. But he does use the gods to make points, about furor as a generally female trait for example (which gets complicated at the end of book 12, when Aeneas goes ape shit on Turnus).
Similarly, Ovid's Metamorphoses make points about the transformations of the gods, but he's largely reworking existing material.