Eternity unfolds across two timelines linked by music and memory. In 1951, the glam-rock star Blue Dot, at the height of his fame, appears on Lightyear Talk Show and sings "Old Nightmare," a song he wrote at seven, as the host introduces a new singer, JJ. When a rocket project is announced to select five works of human music over five years and launch them into space for aliens, Blue Dot sets out to create music worthy of it. Album after album goes unchosen, and his popularity fades. On his next talk-show appearance he is cut off mid-sentence while JJ takes the spotlight. Dismissing his manager, he writes "Eternity," a song about wanting to be remembered forever, and performs it on the stage program Magnetic Highway, but the audience is unmoved and JJ's "Dancing Tonight" is selected instead. Pressed to abandon his glam-rock image, Blue Dot realizes that as long as someone remembers his music, he will not truly disappear.

Seventy-two years later, Kuiper, a lonely young man devoted to the forgotten Blue Dot, composes songs on a stylophone and looks for a place to perform. At a glam-rock bar about to become a taco restaurant, the owner lets him sing one last song on the empty stage and gives him an invitation to Magnetic Highway. Kuiper chooses to sing "Eternity," and like Blue Dot, he at first fails to draw attention, until a television producer offers him a broadcast slot on the condition that he drop the glam-rock look and rely on his voice alone. His rehearsal in a plain suit succeeds, but at the decisive moment he remembers Blue Dot and what the song means. In the final scene the two timelines converge: Blue Dot and Kuiper sit side by side applying makeup, putting on wigs and glittering costumes, and sing together in harmony.