Errol Morris calls it the Rosencrantz and Guildenstern approach to history. “Don’t interview Hamlet,” says the Oscar-winning documentary maker. “He’s going to be, after all, endlessly equivocal. Why not interview Rosencrantz and Guildenstern? It’s a different way into a story, and sometimes a different way in can be really insightful and interesting.”

Morris’s latest work is not, therefore, a biographical film about Timothy Leary, the high priest of LSD described by Richard Nixon as “the most dangerous man in America”. Instead the protagonist is Leary’s ex-girlfriend Joanna Harcourt-Smith, who got high with him in Europe, went on the run with him to Afghanistan and pressed for his release from prison in America.

My Psychedelic Love Story serves up a cavalcade from rock stars to the filthy rich, from counterculture gurus to sinister government agents, as the hopeful flower power of the 1960s gives way to a darker decade: Nixon’s war on drugs, the Watergate scandal and the type of conspiracies and paranoia that infused films such as Three Days of the Condor.

“It’s quite a collection of characters and a portrait, in many ways, of an age,” says Morris, 72, speaking by phone from his office in Cambridge, Massachusetts. “My focus wasn’t primarily on Leary and trying to answer these questions, is he a good man, is he a bad man, did he betray people, did he not betray people?

“I’ve heard over the years a lot of negative things about Leary but again, that’s not the underlying idea of the film. In many ways, it’s a little girl’s story, falling in love and being plunged into this kind of 70s nightmare. It’s interesting for that reason alone.”

Among the film’s beautiful montages and visual effects are recurring cartoon snippets from Alice’s Adventures in Wonderland. With its combination of innocence and trippiness, it is a fitting metaphor for the free-spirited Harcourt-Smith.

She was born at the Palace Hotel in St Moritz in Switzerland in 1946. Her father, a commander in the British navy, died when she was 10. Her mother was a wealthy heiress who “bragged she made love with Mussolini”, Harcourt-Smith recalls in one of many casually dropped eye-popping asides.

She is disarmingly frank about her childhood in Paris. She removes her spectacles and breaks down when recalling how she yielded to pressure and falsely accused a gardener of inappropriately touching her; he was consequently taken to prison. Conversely, when she sexually molested by her mother’s chauffeur, her mother would have none of it, observing coldly: “Good chauffeurs are hard to find.”

Such experiences, Harcourt-Smith says, were a motivation to seek out Leary, a prominent psychologist who pushed the idea that psychedelics could “cure” trauma. She quickly fell under his spell and the fact that he was a fugitive from justice – he had escaped from prison in California, where he had been serving a 10-year sentence for drugs offences – only added to the allure (“I always wanted to be with an outlaw”).

It did not matter that he was 26 years her senior. She says: “I loved him. I had known him for six weeks. We had travelled like shooting stars across Europe, taken acid every day, plunging into the maddest romantic relationship you could ever imagine.”

They went to Vienna and Beirut but on arrival in Kabul were instantly arrested by American agents. Harcourt-Smith poignantly recalls how Leary accompanied her to a hotel toilet in the Afghan capital. “He got down on his knees. I don’t know why it still just makes me cry today. It was such an act of tenderness in that moment that was frenetically terrifying. Timothy getting down on his knees, carefully, minutiaesly [sic] cleaning the toilet. I felt protected in this moment of horror.”

The couple were flown to California where Leary went back to prison. Harcourt-Smith wrote him daily letters, coating the stamps in LSD, and smuggled more acid to him via her belly button when she visited. She was also the public face of efforts to win his release. Eventually, after three and a half years, he walked free – but only on condition that he become a federal informant.

It was regarded as a rank betrayal by the millions he had urged to “turn on, tune in and drop out”. Some blamed Harcourt-Smith for effectively putting a nail in the coffin of the 1960s. Allen Ginsberg, the beat poet, wondered if she was “a sex spy, agente provocateuse, double-agent, CIA hysteric, jealous tigress or what?” In the film she describes how the accusation left her questioning for decades whether she had been manipulated into becoming a government pawn, a “Mata Hari”.

Morris, whose works include The Thin Blue Line and The Fog of War, reflects: “She asks herself, ‘Was I a CIA plant? Was I being used by the federal government in some way?’ Without ever really knowing the answer.

“My guess is that they were involved in some way. It’s a high-profile case. Leary was, of course, of interest to the federal government, enough of an interest that they pursued him to Afghanistan – extradited him or kidnapped him or however you want to describe it – and brought him back to California. So that much is part of the story. That much we definitely do know.”

Leary and Harcourt-Smith tried to begin a new life in a witness protection programme but there was to be no happy ending. They argued and one day Leary suddenly disappeared; Harcourt-Smith still appears puzzled and hurt. At 30, she started over, marrying more than once and becoming a mother and grandmother. But those LSD-fuelled adventures with Leary, which she had hoped would heal past traumas, lingered as a trauma of their own that took decades to get out of her system.

In 2013 she published a memoir, Tripping the Bardo With Timothy Leary: My Psychedelic Love Story. Then she made contact with Morris and he read it. “I thought there was a movie in it, but I can’t say that I had some clear understanding of what that movie would be. I knew I liked Joanna from talking with her on the phone and then the interview turned out to be something unexpected.”

Morris interviewed Harcourt-Smith for about 15 hours over two days last December at a house in Boston using his signature “Interrotron”, a system in which two teleprompters connect to two cameras and allow for the interviewee to look directly into the interviewer’s eyes. The coronavirus pandemic forced Morris to abandon plans for dramatisations and other context, ensuring a tight focus on Harcourt-Smith and her narration.

To go back to his Hamlet analogy, it is a chance to dwell in a long soliloquy. The film-maker says: “It’s something that I very much like: the character that is investigating themselves in the course of the story that they’re telling. It’s true in any good exploration of a character.

“I was asked, I suppose at the time of Fog of War [an epic interview with former defence secretary Robert McNamara], which was done with the Interrotron, are you aware you only interviewed one person, which was kind of heretical, not the way these things are usually done or not the way they were usually done in the past.

“My thought has been if you’re telling a story about a crime, the mystery of who did it or what transpired, you want to interview a lot of people. You want to try to encompass the mystery to examine it. But if you’re trying to examine a person, their underlying psychology of who they are, how they see themselves, better to interview one person and only one person.

“In many ways, My Psychedelic Love Story is a return to that earlier form of constructing a movie. Even though you hear Timothy Leary’s voice and you have an extraordinary tape that came out of Vacaville [prison], it still is a first person story, primarily with Joanna Harcourt-Smith.”

But just as Rosencrantz and Guildenstern Are Dead, it comes as a shock at the end of the film to discover that Joanna Harcourt-Smith is dead. She succumbed to breast cancer last month at her home in Santa Fe, New Mexico, at the age 74. It is hard to reconcile this fact with the vivid, mischievous, luminous presence on screen in My Psychedelic Love Story.

Morris spoke to her two or three days before her death. “I was able to show her the movie before she died and I understand she may have watched it five, six, seven or more times,” he says. “I suppose even nicer to hear than the fact that she loved the movie is that the movie gave her comfort.”

Thanks to Morris, something of her will live on forever on film. He muses: “We have these distinctions between drama and documentary. Sometimes they’re clearcut, sometimes they’re not so clearcut, but there’s this idea that there is no element of performance in documentary and that is just untrue.

“Speaking as somebody who has made a few of them over the years, performance becomes a very big part of them and she’s very much alive in front of the camera in a way that seems quite extraordinary.”

• My Psychedelic Love Story is now available on Showtime with a UK date to be announced