I now pronounce you … Sam Rockwell, John Malkovich and Martin McDonagh.

Photograph: Giulia Parmigiani Interview‘Old-timey fascism was kept secret. Now you don’t have to hide it’: Martin McDonagh, John Malkovich and Sam Rockwell on Wild Horse Nine Xan Brooks McDonagh’s latest film has Malkovich and Rockwell shooting the breeze as CIA agents in 1973 on Easter Island. They discuss grandchildren, swimming with turtles and who shot JFK armuffs!” says Sam Rockwell, pausing his gushing tribute mid-flow and turning to face John Malkovich on the couch. Rockwell loves Malkovich and has been discussing his work at some length. Malkovich, he says, is charismatic and dangerous, half masculine, half feminine; a unique combination and the perfect sparring partner. He’s one of the world’s finest actors and annoyingly modest to boot. “Earmuffs!” says Rockwell and pivots back towards me. “He hates hearing all this. That’s why I keep saying ‘earmuffs’.”Malkovich frowns. “I don’t mind it,” he says.

“Hates it,” says Rockwell. “He truly hates all this stuff.”In Martin McDonagh’s Wild Horse Nine Malkovich and Rockwell play bickering CIA agents who may also be the best of friends. Chris and Lee are fresh from plotting the 1973 coup in Chile and are spinning their wheels on Rapa Nui, amid the crashing waves and the moai statues.

They’ve seen too much and sinned too greatly and now Chris has cancer, which is hardly helping his mood. So he takes Lee aside and asks for one last big favour. “Shoot me in the head on Easter Island,” he says.

Ahead of the film’s premiere, the production team commandeer suites at an opulent Venice hotel and hand out hats and T-shirts to each new arrival. The lobby becomes a sea of merch. The harried concierge has to raise his voice to be heard. He says: “Second floor for the Six White Horses press interviews.”

McDonagh makes films that are playful and volatile, spring-loaded with violence and spiced with absurdist black comedy. Wild Horse Nine nods to In Bruges and The Banshees of Inisherin with its odd-couple antics and explosive side notes. But its mood is more mournful, death-haunted, with one eye on the past. McDonagh – once the upstart enfant terrible of London theatre – is now a silver-haired 56-year-old who comes at life from a different angle. “I’m getting older,” he says. “Maybe this is my first old-man movie.”On sitting down to script Wild Horse Nine, the film-maker wrote GUILT and REGRET at the top of page one, as though setting his course with a compass and sextant. His film opens in Santiago before relocating to the South Pacific. From there it homes in on Malkovich’s CIA veteran, a leaky repository of cold war horror with his memories of the Bay of Pigs and Dealey Plaza. Chris is likely dying and wants to go out with a bang. He claims that he knows who killed JFK and is about to spill the beans.

Photograph: Diego Araya Corvalán/Searchlight Pictures The Kennedy assassination is the God particle of conspiracy theories. It marked the loss of US innocence, or the start of the rot of disinformation and fake news. McDonagh knows the official version and remains breezily unconvinced. “I definitely think there was something going on,” he says. “I’m definitely a believer in the conspiracy. Exactly what that was, we’ll never really know. Was Lee Harvey Oswald involved? More than likely. Was he the lone gunman? I don’t believe that for a second.”He’s made several pictures with Woody Harrelson. Wasn’t Harrelson’s father once rumoured to have been involved in the killing? McDonagh sits up and mimes zipping his lip. “I know nothing,” he says.

McDonagh sits behind one closed door; Rockwell and Malkovich behind another. On-screen or off, the two actors have different energies, different speeds, so that the interview feels like a private performance: the Energizer Bunny versus the all-seeing Sphinx. One of these men has left his sunglasses on the floor. Inevitably it is Rockwell, who is altogether more bouncy and heedless. “My Guccis,” he cries. “Oh man, I would have stepped on those.”On location … the director Martin McDonagh with John Malkovich and Sam Rockwell in Rapa Nui.

Rockwell won an Oscar for playing the bumptious small-town deputy in McDonagh’s Three Billboards Outside Ebbing, Missouri Malkovich may well follow suit thanks to Wild Horse Nine, which goes on to receive a rapturous 13-minute ovation at the premiere. The 72-year-old is on fabulously flavourful form as Chris, a tragicomic monster who is simultaneously melting down and seeing the light, lashing out and making amends. The character plays to the actor’s natural strengths, mining his innate theatricality and enigmatic air. But he explains that the role required some heavy lifting as well. Endless rehearsals and hours of line-readings, he says. “Sam and I did each scene at least a thousand times.”A thousand? Malkovich is so self-contained and unblinking, it’s hard to know when he’s joking.

“You are, too,” Malkovich says. It’s good to have a co-star to rehearse with, he adds, although every good actor has their own way of working. Clint Eastwood, for instance, prefers to hit the ground running. “You have to be a slick talker to get more than two takes out of Clint. You have to be pretty convincing, because he doesn’t take that lightly. As I know from experience.”

They were on Rapa Nui for six weeks, which helped with the process. “I have two granddaughters, so it was a long time away from them,” he says. “I don’t like being away from my grandchildren. But it’s a great place to shoot because there’s nothing else to do. You can swim with the turtles but that’s about it. Your work days are long. You’re always prepping for tomorrow. If it weren’t for a movie, I’d probably go nuts.”

Rockwell enjoyed it. “We had a great time,” he says. “Every night we had a little Chile wine and some rum. And there was a drink made with sugarcane, what the hell was it called? They put an egg-white in it.”His partner, the actor Leslie Bibb, has materialised in the doorway. “Pisco sour,” she says.

“Pisco sour!”He’s delighted to see her and glad of the intel. Bibb has swung by to check when Rockwell breaks for lunch. He introduces her to me and indicates Malkovich on the couch. “But you can’t miss John,” he says. “Look at him, he’s beautiful.”Marooned on his island, Chris plans to write his memoirs and come clean. His bosses are terrified he’ll mention “the Dallas parts” of his story. Some secrets, they feel, must be taken to the grave.

Malkovich has played heroes and villains He’s been Tom Ripley, Biff Loman and the Vicomte de Valmont. But his career has been long and he’s covered this particular topic before. In 1994, he adapted and directed a stage version of Libra, Don DeLillo’s novel about Lee Harvey Oswald. He studied the Zapruder footage of JFK’s final moments and wandered down several conspiracy rabbit holes. The Warren Commission’s findings, he concluded, were either flawed or a lie. And if that makes him a crank, he’s hardly in the minority.

Photograph: Entertainment Pictures/Alamy I’ve read that he hasn’t voted since the 1972 presidential election, when the liberal George McGovern lost in a landslide to Nixon. He nods; this is true. “I’m not a believer,” he says.

Not a believer in what? Democracy? Malkovich shrugs. “In the whole thing, really. As they say in France: ‘Je ne pratique pas’, I’m not practising. I remember the night McGovern lost. I was talking to my father on the phone and I said: ‘Well, I’m done.’ He said: ‘My God, John, you can’t be done.’ I was 19 years old but that was it, I was done. I concentrate on what I can make and leave it at that.”

What about Rockwell? Is he still practising? “Yeah, well, I vote,” he says glumly. “I vote with faint hope. Hoping Obama will come back.”The publicist sticks her head around the door. She reports that lunch is almost ready, which means that we’ve reached the last question. Rockwell perks up. “No pressure,” he says.

Let’s finish with death. That’s where the whole film is leading. Chris has decided he wants to die on Rapa Nui. Then he changes his mind and opts for Venice instead. Assuming that a death can be scripted like a film, where in the world would be the ideal place to bow out?

Malkovich thinks for a moment. “Probably on stage,” he says. “About 15 years ago I toured with a new opera based on Casanova’s memoirs. It started with Casanova chasing a chambermaid around the stage, as he was known to do, and then he has a heart attack. The play stops and people come out with a stretcher and then everyone breaks into song. Before the performance, I always made sure to tell all my friends: ‘It’s just the beginning of the play. I fake a heart attack. Don’t pay any attention.’ But forgot to tell my then-agent and I don’t think she has ever forgiven me.”

A few nights after that, he made the exact same mistake. “I have a friend, Barbara Sturm, who is a knee doctor in Düsseldorf. She came to see me and I suddenly realised I hadn’t warned her either. So I tried to text from the dressing room but of course she already had her phone switched off, being a well-mannered person. And so blah-blah-blah, the whole thing happened again.”

The production was pure chaos, but it was also rather funny. Every night he’d fake a coronary and see the panic sweep through the audience like wildfire. “As many as 20 people would run up to the stage. You’d have the doctors and a stretcher and then everybody starts singing.”Rockwell is laughing. “That’s good acting,” he says.

“Well no, it’s terrible.” says Malkovich. “But still, it wouldn’t be the worst way to go.”