Arquette plays Peggy Newman, whom we meet living in Palm Springs high style, married to Denny (Matt Dillon) and playing hostess to a lively pool party. It’s a happy scene. Then federal agents arrive, and all at once, bags of drugs are being pulled from hiding places and are not quite disposed of.

Ten years pass in the space of a title card. Denny is in prison, and Peggy — who is recovering from an opioid addiction and not recovering from the death of her mother, Rosalyn (Bernadette Peters) — is working as a dance hall girl/stuntwoman in an Old West tourist town in the nothing-posh-about-it Yucca Valley, an inflated, theme park version of the actual movie set Pioneertown, which you can visit when you’re done reading this.

Successful straight-world siblings Dianne (Christine Taylor) and Stewart (Keir O’Donnell) want to sell their late mother’s house, where Peggy, who took care of her, has been living. Despite her insistence that she’s doing better, they are unimpressed by her Pioneertown job, of which Peggy is quite proud, find her insufficiently serious or productive and threaten to withdraw their support. Faced with having to keep up the mortgage, she needs to find a new income stream.

Events lead Peggy to the office of down-at-heels private investigator Bruce (Brad Garrett), who owes money to one of her co-workers. She enters his office in a trench coat and a wide-brimmed hat, like a film noir femme fatale, giving her speech a percussive theatricality — Mae West crossed with Barbara Stanwyck — and more or less confuses him into hiring her as an “unpaid associate.” (She demands a percentage of the work she brings in.) Like Natasha Lyonne‘s Charlie on the not dissimilar “Poker Face” — and most TV detectives, for that matter — she has a gift for reading people.

“Who would have thought at my age, starting this prestigious career,” says Peggy. “I’m like Mary Tyler Moore on methadone.”

And so we are off into a Hydra-headed story that involves Guru Bob (Rupert Friend), a former local anchorman with a mini-cult; a stolen Picasso (Peggy’s knowledge of art history, and the history of art theft, is impressive and unexplained); art forgery; mob-connected brothers Nick (Carmine Giovinazzo) and Leo (Michael Masini), who run a tanning salon and have offered a reward for the whereabouts of their missing sister; and a disgruntled customer of Guru Bob’s, Arman (Carlo Rota), and his sadistic, psychopathic daughter Heather (Julia Rickert), a character that feels a little exaggerated even by the colorful standards of the show.

Arquette and Bernadette Peters, who plays Peggy’s mother.

(Apple TV+)

Ah, but there’s more. There is the sudden appearance of Ginger, a former Hollywood “day player” (she was on “Gunsmoke” and “B.J. and the Bear”), who exactly resembles Peggy’s late mother (Peters again, of course, and very funny.) If this were Hitchcock — or most any thriller, really — this would have some “Vertigo” skulduggery behind it; here, it is merely a miraculous coincidence that inspires Peggy to write a play, to be staged in the Pioneertown theater, “for that catharsis Aristotle talked about. I’m purging all my mommy sh— so it doesn’t give me cancer.” (“It’s going to be like ‘Hamilton’ in terms of word of mouth,” she exults. “It’s going to be a frenzy.”)

And then there’s her friend Carol (Weruche Opia), who thinks she’s been followed by federal agents. And Denny, who gets out of prison and back into Peggy’s life over her half-hearted objections. It’s a very busy eight episodes, and whether it’s because another season is planned, or because life’s just like that, or because they just ran out of runway, not every plot line is fully developed or ends in a neatly tied bow.

The series’ mix of narrative implausibility and emotional veracity is reflected in Peggy’s character. She improvises her way through what she refuses to regard as a disastrous life, walks around rules that make no sense to her, and steamrolls her way over the objections of lesser mortals. This exchange, with her Pioneertown boss, Owen (Eric Petersen), regarding a robbery she wants to solve before he goes to the police, is typical.

Owen: “You have 24 hours.”

Peggy: “I’d like 72. Or four days.”

“Forty-eight hours. It’s two days, but no more.”

“OK, agreed. Sixty hours.”

She’s a logical person whose conclusions are drawn from premises more conventional minds would find faulty. There is a kind of energy and optimism even in her desperation. For all her social marginality, Peggy is the hero here, the most capable character, if only because the challenges she faces, including the ones she sets herself, are more outrageous, dangerous or harder to meet. People depend on her; she’s a force for justice in her little world, even if she’d like to get paid for her work. Peggy is tough, vulnerable, impulsive, clever, scattered, focused, confident and needy, and Arquette — who has been going from strength to strength with central performances in “Escape at Dannemora,” “The Act” and “Severance” — knits these attitudes into a single, singular person whose contradictions never feel contradictory.

Talented actors fill every role. Even as you follow the plot, your thoughts may drift to the players — how Dillon, who finds the sweetness as a hapless ex-con, is a comic actor at heart, and that Garrett has aged nicely since “Everybody Loves Raymond” (and has been showing up in interesting places lately — see also: “Bupkis”) and that Peters, who cannot possibly be 75, is some sort of national treasure. This is a perfectly acceptable way to watch TV.

Created by Nancy Fichman, Katie Ford and Jennifer Hoppe, and directed throughout by Jay Roach, “High Desert” has something of the flavor of “Fargo” — the television series perhaps more than movie — but lighter, warmer, less violent. It would likely be enjoyable with another actor in the lead — in this writers’ strike season, it’s worth pointing out that the script is the foundation of the performance — but perhaps not quite the layered, surprising, surprisingly moving experience Arquette makes it.