In 1984, a billboard featuring a pouting, pneumatic blond woman appeared on Sunset Boulevard, the most feted thoroughfare in Los Angeles. “Angelyne rocks,” it declared. There was a phone number and nothing else. Any onlookers curious enough to call got through to her management: would they like to book Angelyne? I don’t know, those callers would probably have answered, who is Angelyne? Within a decade, there were 200 Angelyne billboards around LA – and still it was no clearer who Angelyne was or what she did. “I’m famous for being on billboards,” she told one bemused interviewer.

Over the years, not much more was learned about Angelyne. She came from the midwest, she said, sometimes mentioning Idaho. There were no romances, no children. She sang in a punk band, did some art. Angelinos might see her driving in one of her many pink Corvettes, sometimes stopping to pout on the hood, or sell photos and merchandise. Investors, she said, were paying for the billboards, and the returns became obvious when she began appearing on screen.

She played a “Busty Lady” in The Frisco Kid, and her cleavage caused a car crash in Earth Girls Are Easy. Her billboard turned up in the opening credits of Moonlighting, then The Simpsons, then BoJack Horseman. She sang with Moby in the We Are All Made of Stars video and became a mainstay in disaster flicks: in The Day After Tomorrow, a flying Angelyne billboard takes out a Fox journalist; in Volcano, her billboard is struck by a fiery ball of lava and explodes. Somewhere along the way, Angelyne became an LA icon, the scrappy starlet who embodied everything that kept the city running: glamour and seediness, heartbreak and chutzpah.

Now she’s the subject of a new miniseries called Angelyne, with Emmy Rossum playing her alongside Martin Freeman and Hamish Linklater – which is why Angelyne is chatting to me today. “Are we on?” I hear her murmur, her Zoom window a wall of pink feathers. Then the feathers flutter up and there she is, wearing a black and silver leotard with pink elbow-length gloves. You look amazing, I say. “Well, you look pretty darn good, too,” she replies. “But you know what? It’s business for me. Gorgeous skin is my business. My astrologer would always say, ‘Angelyne, you have the most beautiful skin.’ She lived to be 104, you know that?”

When that first billboard went up in 1984, she says, “it was like BOOM! But to me, being huge is normal. I do well big, I do well at 100ft. Wherever I came from, whatever is core to me, I was born with that.” She was soon inundated with requests – “from regular fans, naughty ones, X-rated authors, TV shows, newspapers, films”. And the rumours started too. She rattles them off: “I’m married to a sheikh. Maybe I am a man. My husband paid for everything. A gay guy died and left me all his money. There is a new Angelyne every two years. I’m a prostitute. I was a mystery.”

In 2017, the Hollywood Reporter (HR) announced it had in fact solved the mystery: Angelyne was really Ronia Tamar Goldberg, born in 1950 to two Holocaust survivors. The Goldbergs had met in the Chmielnik ghetto in Poland and endured horrors at various concentration camps. After the war, they married, then took their daughter to Israel before settling in the US. Her father was controlling; her mother died of cancer when she was 14. HR had been tipped off by a “hobbyist genealogist”, who thought it would be “fun” to discover Angelyne’s story.

“Angelyne’s real identity is finally solved,” the headline ran. But did anyone truly need Angelyne’s identity to be solved? Why couldn’t Angelyne simply be Angelyne? HR granted the genealogist anonymity, while printing his reasoning that “she forfeited any claim of privacy when she ran, as a stunt or not, for governor of California”, in 2003. Even her ex-husband is quoted as saying she never talked to him about her past. “If I brought it up, it was shut down,” he told HR.

“Strangely enough,” the New York Times once observed of Angelyne, “she seems to evoke the most hostility from the men whom her sexpot persona would seem to be trying to please.” Certainly, over 30 years of interviews, numerous male journalists have complained that she hasn’t told them the whole truth, or they’ve made snide remarks about her $20-a-photo fee and her merch-hustling.

Since the HR story ran, Angelyne has complained vaguely about “inaccuracies” in it, without totally denying she is Goldberg (or was, in another life). More often than not, she has just seemed peeved that someone else got in first. Having control seems important to you, I say. “Control is important to everybody,” she replies, a bit snappishly. “It’s not important to you?” Sure, I say, but I’m not famous – no one has ever said I’m not entitled to privacy.

Angelyne is quiet for a moment. “It was horrible,” she eventually says of the article. “What do I say when somebody comes up to me crying, saying, ‘I relate to what happened to you?’ I mean, what do I say – ‘I’m sorry, that’s not true?’ I don’t have the heart to do that.”

Gary Baum, who wrote the story, told the Guardian: “I reported information available in public records.” He added: “Since my article was published nearly five years ago, Angelyne has never substantively challenged its facts .” Drawing on his piece, the show veers between drama and mockumentary. Rossum reportedly spent up to seven hours having prosthetics – including an enormous breastplate – applied. Freeman, meanwhile, plays a fictionalised version of Hugo Maisnik, the wealthy entrepreneur and printer who created the first billboards.

The fact that the miniseries draws on the HR article worries Angelyne. “There’s only one Angelyne, and I’m concerned that show might mislead people.” Did she talk to its makers? “I refused,” she says, then laughs. “But they gave me a lot of money – millions – because my name is trademarked. They couldn’t do it without me.” Although she has no formal credit on the show, she says: “They wanted to make me executive producer. And I initially agreed because I didn’t know it was gonna be so bad.”

What does she think of Rossum’s portrayal? “It’s a bad pastiche. You know, they’ve tried to do Marilyn Monroe so many times and they could never get it right. But Marilyn was an actress – whereas I made myself. I don’t want to watch it. It’s disturbing to see someone misrepresent a beautiful artwork. She’s got a long face.”

We’re speaking by phone now and the line cuts out. When I call back, Angelyne sounds chastened. “You know why that happened? The universe hung up, because I started being very childish.” She adopts a babyish voice: “She’s got a long face.’ The universe said, ‘No, no, no!’ I try to stay positive.” She has another go at explaining her feelings: “I’m an artist. I paint in the mirror. Everything has to be perfect – my eyes, my nose, my mouth. And for someone to take that and mess it up is painful. I can’t even watch it.”

She is working on her own film, Angelyne: Billboard Queen, which will explain “what happened to me as a child, how I made it, how I talk to the men in a man’s world”. Would she have made this film if other people weren’t trying to tell their own version of her story? “I was planning a film, but I wasn’t in a mad rush. I have a lot of footage, 100,000 pictures. You are gonna love my film! It’s gonna transform you. It’s The Godfather of films.”

Do people sometimes forget that, under the big hair and the eyeshadow, there is a real person? “But I’m an alien!” she says airily. “I came to this planet to help everybody. And this is probably one of the most difficult planets in the whole universe. There is a lot of pain, a lot of problems, but every problem comes with a solution. And I’m the solution.”

Back in 1987, she said in an interview: “It’s so much fun being famous for nothing.” It’s a line that now seems prescient: we’re used to people being famous for nothing. “I had to say nothing then,” she explains, “because people wouldn’t understand. I’m not famous for nothing – I’m famous for my essence. I’m sitting on top of a pink cloud, sending inspiration to the world. The difference between me and other famous people is that I’m only attached to Angelyne. I don’t do endorsements. I want my image to be clean – clean, clean for Angelyne.”

She doesn’t like being called an influencer, feeling the term “is used too much. I like ‘inspiration’. You know, the Kardashians, Paris Hilton – what have they done? I’ve talked to Paris, she’s very sweet. But so what? Kim said something nice about me. Good! But they don’t impress me. Nobody but Barbie impresses me. She’s open to anything because she doesn’t have any emotion. She can say, ‘Who cares? So what?’ She’s plastic. I love her.”

Occasionally, Angelyne allows glimpses of vulnerability. At one point, she tells me about a meeting she had with the executive of a billboard company. “He said to me, ‘Let me undress you and you can have all the billboards you want.’ From all the different attempts I’ve had on me, in that sexual arena, I developed a phobia. I have to always have a door unlocked – I have to know I can get out. I’ve been in huge studios with major executives and they’ll still try and pull something sneaky, you know, because I’ve got blond hair.”

Who is Angelyne really? Well, someone it is near impossible to get a grip on. But maybe who she is is up to you. To cheer her up, I tell her that a friend of mine in Sacramento regularly sees her driving around in her Corvettes and considers her a lucky charm. “I want to see Angelyne, too,” sighs the starlet. “I’d like to have a lucky day. I need my own Angelyne.”

She asks when I’m coming to LA. “I’d love to give you a ride in my car. You’ll get all the attention you’ll need for the rest of your life.” And then it’s “Big hugs!” and she’s gone.

• Angelyne starts on Peacock in the US on 19 May, on Stan in Australia on 20 May and airs in the UK in the summer.