In the story, the "squirming coil" represents the sunset. That is stated explicitly in the opening line, "The squirming coil of sunset."
Satan is referred to once ambiguously with the line, "I saw Satan on the beach." Satan is referred to again more subtly with the line, "Jimmy holds the tannis root." Tannis root is a fictional herb that appeared in the 1967 novel Rosemary's Baby
and in the 1968 film the book spawned. The story is about a woman who is tricked into giving birth to the Devil. Tannis root is mentioned multiple times in the film and is secretly fed to Rosemary.
Satan on the beach tries to catch a ray of the squirming coil (meaning the sunset), but fails.
Another reference to the sun is made with a line about Icarus "with melting wax and feathers brown." Icarus is a character from Greek mythology who flew too close to the sun, which melted the wax in his wings and sent him plummeting to the sea.
None of it seems to make any real sense, but Phish.net says
the song is cautioning listeners against "seeking favor, fortune, or fame, at any price." To grasp that, we just need to ingest the tannis root - difficult, unfortunately, because it doesn't actually exist.