NEW YORK — I’m running a little late as I make it over to the Laura Pels Theater on 46th Street. When I get there, a tiny crowd surrounds Jake Gyllenhaal, bearded and maned for his performance in the off-Broadway play “If There Is I Haven’t Found It Yet.” He’s almost unrecognizable, which goes a long way toward explaining why the crowd is tiny. He’s gracious, all smiles, answering questions.

Later, backstage at the theater, he recalls what it was about the piece that made him finally break his long hiatus from the stage. Written by Nick Payne, the George Devine Award-winning play features Gyllenhaal (in his New York theater debut) as Terry, a loafer uncle to an affection-starved, overweight teenage girl. It’s a quartet piece but Gyllenhaal shines, largely because of his character’s idiosyncratic nature. That nature was founded in the play’s dialogue, which Gyllenhaal says was like trying to unlock a Rubik’s Cube.

“The character stops in the middle of thoughts and he continues into the middle of the next one,” the 31-year-old actor says. “Sometimes he’ll pick back up parenthetically like four or five lines back down. So you don’t just have to find the attention, you have to fill in the blank…The story is so obtuse; it’s the same thing. You begin at the middle of the scene and you finish before the situation actually ends. So to me, I was just fascinated by that and it started to guide me.”

Gyllenhaal says he always felt comfortable in front of a live audience and, ever since he was a kid, enjoyed mimicry. A cockney Brit was one of his “stock characters that are always used as caricatures that aren’t really necessary,” he says. “They’re kind of like the simple shape and form and mold of a sculpture.”

The language itself, though, the rhythms of it, made the part irresistible. He could even see the architecture of the dialogue for each character on the page. All of Terry’s dialogue is on the left side of the page, never making it past half-way across. The starting and stopping gives tangible shape to the thing, and as to informing character, it almost serves as a defense mechanism. As the play’s director Michael Longhurst put it in a telephone interview, “When characters speak like that, it’s often to avoid what he’s trying to say. He spends his time asking people how they are. It’s a way of avoiding how he’s doing. It’s a very British thing to do, deflect, deflect, deflect.”

And so Gyllenhaal starts in with his accent to illustrate the point: “When I first come in I’m like, ‘Probably should have rung or something,’ period. ‘But phone was fucked,’ period. ‘And I thought,’ period. ‘By the time I was trying to get change for the fucking,’ period. ‘You know, the phone and that,’ period. ‘Then I might as well just,’ period…It’s crazy! But that’s the way he writes, and unlocking it is what’s fun.”

All of that makes for lengthy introduction to how language and behavior was the key to success when Gyllenhaal signed on to play a Los Angeles police officer in David Ayer’s “End of Watch.” A new spin on found footage (though that’s not really what this is — Gyllenhaal’s character films much of his exploits and so that point of view becomes diegetic for the film’s purposes), “End of Watch” tells the story of a pair of patrolmen who spend their days on the southeast side of LA going after gang-bangers and drug-pushers until one unfortunate day, they open too many doors and find themselves the target of a Mexican drug cartel.

Gyllenhaal was looking for something new in his life and, according to Ayer, chased the project down. “I think he was just frustrated,” Ayer said by telephone. “He wanted to act. He wanted to just sink his teeth into a role and act and not be distracted by the sort of big business side of things. He wanted to lose himself and he wanted to be reinvented…He’s just like, ‘Look, I’m sick of everything. I’m sick of my life and I want to change it. I want change.’ And that’s all I heard, is that he’s ready to transform. His heart was really open at that time and he was really receptive to doing something totally different and giving me the total commitment that I needed for this movie to work…I told him, ‘Look, if this works out, you’re going to come out of this a different person.’ And I think that happened.”

Here was an immersion of a whole other sort. For months Gyllenhaal underwent tactical training and participated in police car ride-alongs with co-star Michael Peña. And again, the way his character spoke was key to who he was.

“There were things Dave would write, where, for instance, there was a speech where I ‘m talking about going on dates,” Gyllenhaal says, before reading off some of the scene: “‘I get laid without a badge, thank you very much. There’s a pattern here, an MO. First date, respectful kiss. Second date’s dinner.’ And Dave was like, ‘Enunciate.’ And when we were rehearsing he’d be like, ‘Enunciate. Enunciate. Enunciate.’ And then I started to realize that the thing about this guy was everything he said, when he talked to people, was very clear. This is going to happen. That’s going to happen. And that all definitely went into it.”

As he describes the philosophy his voice mimics what he’s talking about, crisp, precise, a 180 from the bubbly Brit he was just moments before.

The ride-along aspect of the prep was particularly crucial. He and Peña did two or three each week for five months. The first call he went on, someone was murdered and died right in front of him. There was a domestic violence call that didn’t turn out the way he had expected at all when they “rolled up on two dudes,” he says. “And it was brutal. The crazy thing to me was watching two police officers switch from their relationship to getting the call and the focus in that. Watching human behavior, for me, it just blew my mind. That was the hardest thing for Mike and I to get, that switch. And Dave talked about it all the time, but watching that was crazy, every time, because it was like sort of fun or just interacting, normal, joking, normal, joking [and suddenly] life and death.”

He admits he had trouble shaking it all off when he’d return from the experience on multiple occasions, noting the under-considered effect of post-traumatic stress disorder in law enforcement officers. “It would take me two or three hours to get to bed, to finally just chill the fuck out,” he says. “By the end, we’re seeing murders and shootings and it just became something normal. I was very surprised at how desensitized I became, and Michael and I talked about that a lot.”

For an actor like Gyllenhaal who — he admits — can be a bundle of energy on set, it must have been a major gear shift. At a recent New York cocktail gathering for his new film “Life of Pi,” Ang Lee — who directed Gyllenhaal to a Best Supporting Actor nomination for 2005’s “Brokeback Mountain” — recalled that energy. “He provided a lot,” Lee said. “He has a good heart. But,” he offered with a smile, “I think when the camera’s rolling, an actor should conserve their energy.” (More on how that philosophy impacted Gyllenhaal in our sidebar on his work with top-tier directors over the years.)

Sam Mendes, meanwhile, who worked with Gyllenhaal on “Jarhead” the very same year, told HitFix that “as a person [Gyllenhaal is] a bit more of an unexploited bum. He”s got much more rage and kind of anger in him and complexity. And so it was a mixture of that sort of youthful, big-eyed innocence and then something else…I think that he”s got a streak of madness in him.”

For Ayer’s part, he made sure he got the most out of that spirit and vigor. “Let’s put it this way,” he said. “The days are so long and grueling that whatever energy he had I made sure got diverted into the movie. So there wasn’t a lot of time to sit and think and bullshit. The work velocity was so intense that you had to bite down and run…and he was locked on.”

One important element, though, was establishing a camaraderie between Gyllenhaal and Peña. And it wasn’t an easy task. “It was like kind of an arranged marriage of sorts,” Gyllenhaal says. “At first, Dave was like, ‘Get together; you’re supposed to be best friends.’ And we’re like, ‘Uh, okay.'” But things needed to get heated if they were going to hug it out.

Gyllenhaal repeats an oft-told story about a tactical training exercise he was doing with his co-star that involved live ammunition. Due to ear protection, they couldn’t hear each other well. “I was shooting and he kept shooting and I started to get pissed,” Gyllenhaal recalls. “And we came out and we like had it out. We just went at it. Then we stormed off and he called me the next day and was like, ‘Hey.’ I was like, ‘What?’ And he was just like, ‘You know, it was kind of cool.’ And I was like, ‘You’re an asshole.’ And he was like, ‘I think we’re friends now.’ It was a quintessential moment where as soon as we went that far with each other, from that moment on it was like, ‘All right, if I can hate you, I can love you, and that’s it…I got your back.'”

The multi-camera technique was another challenge, but it was mostly fun and opened doors for the actors. There would be cameras rolling pretty much all the time and Gyllenhaal says they had something like 135 hours of footage when all was said and done.

“Dave would call ‘cut’ and everyone would go off and Mike would be doing shit that was brilliant,” Gyllenhaal says. “He’s so funny and he’s like in it, we’re still in it. So I just put the camera on him and I’d be like, ‘Let’s roll sound,’ and we’d roll sound, and I would just press record on the camera and I’d film Mike doing this stuff. It was gold! Our editor, Dody Dorn, was brilliant that she could even put it together.”

At the end of the day, Ayer got exactly what he wanted out of the actor, and the actor got exactly what he wanted out of the experience. “He has a good heart,” Ayer told me, “and that’s why I thought he was so right. Because sometimes you cast this stuff and it’s this action hero vibe. I didn’t want an obvious cop. You don’t cast a guy you feel like is a cop. You cast a guy who feels like a dude, a normal guy, a normal person with depth, and then turn them into that cop. So this character, you can feel the curious mind and the soul and the emotional life behind the demeanor of a law enforcement officer, a ghetto gunfighter.”

And finally, says Gyllenhaal of Ayer, “That motherfucker changed my life. I don’t know how to put it any other way. He took this kid, who had, like, grown up in LA, relatively easy lifestyle, and he threw him into a world that I definitely had preconceived notions about and had my own stigma about, not only with law enforcement but also southeast LA, all that, and he just blew it open. He just showed me a place that he called home, that changed his life, that made him who he is…There was no safety net. And I think that in a majority of life lived with safety nets, someone who pulls that out and says, ‘That’s for real. Are you ready for this?’ That changes your life.”

“End of Watch” will be returning to theaters nationwide on December 7 in a re-expansion. It arrives on DVD/Blu-ray on January 22. Meanwhile, “If There Is I Haven’t Found It Yet” resumes performances at the Laura Pels Theater in New York and plays through December 23.

(Check out our sidebar discussion with Gyllenhaal concerning what he’s learned from the many talented directors he’s collaborated with, from Ang Lee to Sam Mendes, David O. Russell to David Fincher.)