Jake Gyllenhaal is happy to finally have a day job.

“Being onstage pretty much every night, sometimes twice a day, is a wonderful consistency that I haven’t really been used to,” the 31-year-old actor said of his off-Broadway play, “If There Is I Haven’t Found It Yet,” which was just extended through late December at the Laura Pels Theatre.

In the play by Nick Payne, Mr. Gyllenhaal, making his New York stage debut, plays Terry, a drifter who drops in on his brother’s family and develops a friendship with his niece, Anna (Annie Funke). Terry scrutinizes the family’s destructive effects on Anna, whose mother (Michelle Gomez) is consumed by her work and whose father (Brían F. O’Byrne) is obsessed with environmental activism. All the while, water slowly seeps onto the stage, eventually submerging actors’ feet and ankles.

Mr. Gyllenhaal, who has also been garnering strong reviews for his role as an LAPD officer in the new film “End of Watch,” spoke with the Journal recently about his first month onstage, shifting his craft from film to theater, and trying not to get waterlogged.

How has the first month of your first New York stage show gone?

I feel like every night it’s not only been a lesson creatively for me, but somehow, some way, just in my life. It’s an interaction with an audience which always has a different personality every night, so there are the nights where you get lots of laughter, and there are nights where there’s nothing. It becomes a lot less about reactions than really trying to tell the story as truthfully as possible. As a film actor, that’s not always your job. Your job is to help the director and give him or her the best possible performance and interpretation, so that they can then tell the story. But in terms of a live performance, it’s up to you and the rest of your cast to tell that story every night.

How else have you found that the play differs from being on a movie set?

On a film I think it’s all about preparation because game day is every day and you only have an instant within which to communicate something specific. Maybe not an instant necessarily, but definitely a shorter period of time. Whereas developing a character in a play, you have three or four months where you’re exploring new ideas. I never just stick in and say, “that’s just the way it’s going to be.”

How are you holding up physically? Onstage you’re hauling furniture and walking in water.

[Laughs] I don’t really think about that. Just given the experience I’ve had, even preparing for “End of Watch” and the police officers—the hours that they spend, the work that they do. My job just seems absurd, and the work and the time I put into it always seems a pittance in comparison. I try to feel great every night and I honestly feel blessed. Four hundred and fifty people actually fill up that auditorium every night to come see our show. All of us have been sick at one point or another, and we actually end up turning out better performances when we’re more tired or our bodies are physically pressed.

There’s a lot of profanity in “End of Watch” and in the play. Do you find yourself dropping more curse words in your personal life?

I have found that at times. Sometimes, weirdly, particularly when you’re doing a play, people say a line that sounds like a line you said in a play, and your response will be strangely similar, or the rhythm will be. I’ve done a lot of interviews recently and sometimes in those interviews, someone will use the same type of phrasing, or words that are connected in the same way that another character speaks to me in the play, and because I do it every night, so often, I’ll throw in some curse words by mistake.

What did you observe firsthand about the way cops are regarded?

When you see two people entering a situation as first responders that they will have very little jurisdiction over after they leave that area, and then also they have no idea what they’re encountering before they even get there, I think you start to understand why, out of context, police officers at times have been given a bad rap. That’s not to say everybody’s always behaved well, I’m not saying that. But I am saying that in general, many of the police officers we worked with always joked that everybody loves firemen, and everybody dislikes the police. My opinion of it is that there is a huge stigma that comes with that uniform, whether you are watching it come towards you or whether you’re wearing it. I’ve had the privilege and opportunity of wearing it, and what I tried to do was spend five months on the street to try and take that stigma out of putting it on and having it feel like a batsuit. Every time I look into a cop car at this point, I see two beating hearts. Two human beings with a history.

You and Michael Pena spend a lot of scenes ribbing each other. Did you ever go off script?

The biggest reason I was drawn to the project was because of the dialogue between these two guys. The heart of the movie exists in that car, and a lot of the things that David [Ayer] wrote are in that car, and were written that way. I would say 90% of the movie is written and that dialogue is Dave’s. Then I would say another 10% of it is me and Mike giving each other crap and enjoying little things in the middle of Dave’s dialogue. But there’s only one scene that is fully improvised – the scene where he asks me if I’m going to marry a Mexican girl, and we start talking about coffee, and I talk about his mother’s quinceanera and his kids’ quinceanera. That whole scene is completely improvised, but in a way it’s not improvised in that Dave wrote us both back stories that were four pages long. Because we had spent five months preparing for the movie, and had spent so much time together, particularly me, Michael and Dave, a lot of that is Dave. Dave’s wife is Mexican and he grew up in South Central L.A. and he was raised by a lot of Hispanic culture. He has such a deep, profound respect for Hispanic culture. He would always say, when are you going to marry a Mexican girl? So Mike used that. And Mike and I would always get coffee, after or before anything we were doing. I would go and get him coffee or vice versa, so he jokes about that stuff, but he is actually so particular about his coffee and his coffee-drinking, so he’s actually the one that’s so particular [laughs]. It all came out of real stuff. So it was improvisation but somehow it was written also.

Tell us about your next project, “An Enemy.”

We finished production on it at the end of July, and then I went right to rehearsals for the play. Denis Villeneuve, who directed it, is cutting it now. I play two roles in “An Enemy.” It’s actually the story about a man who is married and his wife is pregnant with their child. He, at the same time, in another personality is having an affair, and there are two personalities and he needs to reconcile the two in order to make a commitment to his marriage. It’s his journey reconciling both sides of himself. At the same time, it’s a thriller on this whole other level, where there could be actually two people. What happens is a question of identity, when you meet yourself. So, there are two things going on but if we succeed at pulling that off – it was a fascinating process, and a very technical process, which I really enjoyed.

Are you signed on to play a detective in Villeneuve’s next film, “Prisoners”?

I don’t know exactly. We’re talking about it, yeah. I hope so and I loved working with him and if I get to work with him again, it’ll be really exciting. It would be an evolution because my character [in “End of Watch”] does say, “I want to be a detective.”

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