Jake Gyllenhaal and Brian F. O’Byrne don’t seem to have too much in common.

One is a 45-year-old Tony Award-winning Irish-born character actor and stage veteran. The other is a 31-year-old A-list movie star making his U.S. stage debut. But spend some time with them and you might swear they’re related.

“He’s like my older brother, that’s how it feels,” says Gyllenhaal, sitting beside O’Byrne in a comfy downtown cafe. “It feels like that in the scenes and it feels like that when we come offstage.”

Fittingly, they portray estranged siblings in the American premiere of “If There Is I Haven’t Found It Yet,” a lovely off-kilter play that opens Thursday off-Broadway about how frustratingly blind people can become.

As if to illustrate how close the duo have become, both arrived at rehearsals clean-shaven but now sporting bushy beards. “As much as it seems like a character choice, neither of us likes shaving,” O’Byrne says and the pair crack up.

In the play, Gyllenhaal adopts a very convincing low-class English accent to play a slacker with a puppy dog’s heart, while O’Byrne, who abandons his Irish brogue for an upper-class accent, plays his professor brother. When the younger man shows up at his sibling’s house, old and new wounds are opened.

During the course of lunch, there is absolutely no ego on show. The actors goof on each other, share compliments and food. Gyllenhaal instantly worries about his co-star’s comfort when the Irishman arrives at his outdoor table slightly sweaty.

“You guys want to go inside? There’s a beautiful table over there. It would be cooler,” Gyllenhaal asks. He then proceeds to expertly carry four filled water glasses to the new table and makes sure everyone is satisfied with the new area.

“He likes organizing things,” O’Byrne teases.

The two had never worked together before but knew of each other’s work. Gyllenhaal had watched O’Byrne onstage in “Doubt” and “The Coast of Utopia” and on TV in “Mildred Pierce.” O’Byrne was a fan of “Brokeback Mountain” and “Donnie Darko.” Now they share a dressing room.

Gyllenhaal says he couldn’t be more lucky to have someone of O’Byrne’s stature as he makes his American stage debut. The younger actor has been itching to get back to theater since he appeared in a revival of Kenneth Lonergan’s “This Is Our Youth” in London in 2002.

“To have a first is a really wonderful thing. And to have a first with someone who is so wise and experienced is a blessing,” says Gyllenhaal of O’Byrne. “It’s an honor working on the stage with him.”

O’Byrne responds with a mock insult – “He’s a one-trick pony, beard or no beard” – and makes fun of Gyllenhaal’s luscious head of hair. “Look at that hair! I mean, have you ever seen anything like it? I could eat it.”

Eventually, the laugher dies down and O’Byrne grows earnest, asking Gyllenhaal to cover his ears while he says nice things. “To have somebody who’s obviously at the top of his game, who comes to the stage with the freshness he does? You don’t often get that,” he says. “It’s great fun.”

Gyllenhaal, whose new film is the cop drama “End of Watch,” got this latest project off the ground when he read “If There Is I Haven’t Found It Yet” two years ago and fell in love with the “architecture of the words.”

He was in London for one day in February when his agent suggested he go that night to see “Constellations,” another of Payne’s plays. Gyllenhaal did, loved it – “it was so precise, so sharp” – and the next morning managed to have breakfast with the playwright. Within a month, the revival of “If There Is I Haven’t Found It Yet” was set up.

He heard the script was being sent to O’Byrne and crossed his fingers the older actor would agree. “As soon as I heard he was going to do it, I was so excited,” Gyllenhaal says.

“It’s been a really wonderful thing to have Brian there to be able to guide us. Not only in scenes. Not only as a tremendous actor. But as somebody who I can turn to and say, ‘Is this supposed to happen?’ And he’ll go, ‘Yes, it’s supposed to happen. And later it will be like this.'”

They’ve also since learned that the first show each saw on Broadway was the same – “Anything Goes” with Patti LuPone in the late 1980s. (“I, by the way, was 8; he was 40,” Gyllenhaal jokes.) And they have learned that they are both actors who revel in the reality of scenes.

“He listens to my rants and he guides me and calms me down and also jacks me up,” says Gyllenhaal. “It feels safe even within the danger of the moment.”