Most people in the theater world run to the spotlight. Not Terrence McNally. Modest, shy and industrious, he’s let his work speak for itself. Fortunately, his plays — “Lips Together, Teeth Apart,” “Love! Valour! Compassion!” and “Master Class” among them — have plenty to say.

But lately he’s been trailed by microphones, cameras and lights as the subject of the documentary “Terrence McNally: Every Act of Life,” for which director Jeff Kaufman interviewed many of McNally’s friends and colleagues, including Nathan Lane, Angela Lansbury, Audra McDonald, John Kander and Chita Rivera.

Kaufman met McNally while the director was making “The State of Marriage,” about the struggle for marriage equality. Much of that film is set in Vermont, the first state to allow civil unions. McNally and his partner, producer Tom Kirdahy, were married there in 2003, and make a brief appearance in the movie.

“Talking to Terrence, I thought it’s funny no one’s ever done a film about him,” says Kaufman. “I think he was reluctant because he doesn’t like to talk about his personal life. But I have to say, he didn’t hold anything back. It’s his story, but it’s also a portrait of what life is like in the theater.”

And not only that: McNally’s life is, in many ways, the history of New York City over the past 50 years. If you want to know what Greenwich Village was like when writers, actors and painters haunted bars and cafes that are now five-star restaurants, he’s got the stories.

He came to New York — from segregated Corpus Christi, Texas — in 1956 to attend Columbia University, where his teachers included Mark Van Doren and Eric Bentley. At a party one night he met Edward Albee, who’d just written “The Zoo Story.” At about 2 a.m., Albee invited him to his apartment for a drink.

“I said, ‘What about your wife and children?’ ” McNally recalled a few months ago at the unveiling of Albee’s caricature at Sardi’s. “Shows you what my gaydar was like back then.”

They lived together near Abingdon Square Park while Albee worked on “Who’s Afraid of Virginia Woolf?” Their relationship, fueled by much drinking in local bars, was stormy. When they broke up, Albee said, “Stay away from the West Village!”

Eventually, they reconciled. McNally was one of the last people to visit Albee before he died in September.

McNally’s own career took off with 1965’s “And Things That Go Bump in the Night,” which Kaufman says “may be the first play to put an open and positive gay character onstage.”

McNally had his ups and downs. At one point, he told an interviewer, he had $400 in the bank. Alcohol nearly destroyed him.

“I had stopped writing,” he says in the documentary. “I spent more time drinking. I wouldn’t be alive today if I had gone on drinking.”

Once sober, McNally solidified his position as a major American playwright with “The Lisbon Traviata” in 1989, followed by “Lips,” “Love!” and “Master Class.” (Musicals such as “Kiss of the Spider Woman,” “The Full Monty” and “Ragtime” helped boost his bank account.)

Kaufman expects to show his film to distributors in June. Here’s hoping it opens the Tribeca Film Festival.