AMAZING GRACE: Crowned with a Philip Treacy wimple, Jones performs “Williams’ Blood,” one of her most autobiographical songs.

Donna Summer’s musical is up for two Tony Awards, The Cher Show comes to Broadway this fall, and if a Grace Jones musical should ever open on The Great White Way, it might look something like Grace Jones: Bloodlight and Bami, the new documentary that hits South Florida theaters this week.

“Bloodlight” is Jamaican patois for the red light that toggles on in a studio when a performer is recording, “bami” means “bread,” and Grace Jones, the world’s longest-reigning androgynous pop icon, has been nourished by both: the glare of the spotlight and the (ostensibly) simple life with her family back in Jamaica.

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Director Sophie Fiennes (yes, Ralph’s sister) refers to these two sides of Grace’s persona as the “anti-natural” and the natural. And over five years of filming, she captures plenty of both elements, traipsing between Tokyo, Paris, Moscow, London, and New York for tour dates, recording sessions, parties, and public appearances, of course, but also tagging along on family visits to Jamaica, including a road trip with Grace and her son Paolo to Spanish Town, where she grew up.

Given Grace’s peripatetic lifestyle, with its sometimes jarring venue changes — Fiennes cuts from a scene of nightclub debauchery to an early-morning visit to church in Jamaica with mom — it’s the film’s musical sequences that supply the through line. The shows, including live performances of “Slave to the Rhythm,” “Pull Up to the Bumper,” and “Love is the Drug,” are, in typically Jonesian fashion, spectacular — as much performance art as performance. Yet it’s during these scenes that she seems to come most fully to life. The stage, with all its artifice, really does seem to be Grace’s natural habitat, and it’s there that we see her most clearly. As Jones once confided to Fiennes, “The music says more about me than I can say about the music.”

Grace first met the director at a preview of Fienne’s earlier film, Hoover Street Revival (2002), which told the story of Jones’ older brother Noel, a charismatic L.A. preacher. “You understand where I’m from,” an exuberant Grace told Fiennes after the screening. “I love the smell of your film.”

Readers, I think you’re gonna love the smell of this one. So, head out to the theater and douse yourself in some Eau de Warm Leatherette.

Grace Jones: Bloodlight and Bami (1h 55m) is playing at O Cinema Wynwood (90 NW 29th St, Miami; o-cinema.org) and opens Friday, May 11 at the Classic Gateway Theatre (1820 E Sunrise, Fort Lauderdale; classicgateway.com).