On the first full day of tech rehearsal for “Kiss My Aztec!” at Berkeley Rep, you could go long stretches without being aware that Tony Taccone is the one in charge.

He’s liable to drift around the set during breaks, as if trying to immerse himself in its world, evaluate it, draw something from it. When his cast of 11 return for a run-through of the opening number — a hilarious take on what it meant when conquistadors first alighted on Aztec shores — he might gently shift his weight back and forth, poised to make a point if necessary, but otherwise ceding the floor. Collaborators such as choreographer Maija García give more direction than he does — which isn’t at all uncommon in tech, much of which is dedicated to designers’ needs. But there’s a striking lack of tension in the room, which surely comes at least in part from its leader’s comfort in his own skin, in both his position and his imminent departure from it.

Taccone will step down from the company he’s been with for 33 years, 22 of them as its artistic director, after he directs this world-premiere musical, for which he also co-wrote the book, with John Leguizamo. It’s been an astonishing tenure, one that’s helped cement Berkeley Rep’s and, by extension, the Bay Area’s reputation for theatrical muscle. He’s brought the same eye that once commissioned, with Oskar Eustis, “Angels in America” to continue to develop and launch shows that influence the national conversation about what the art form is and can be: from Stew’s “Passing Strange” and Jackie Sibblies Drury’s “Fairview” to Green Day’s “American Idiot” and Anaïs Mitchell’s “Hadestown.”

Yet for all those accomplishments, Taccone’s the kind of person whom an actor can call “T Squared,” the kind of person who proudly displays in his office a painting his son commissioned from a Vietnamese artist fusing Taccone’s likeness with that of Al Pacino in “Scarface.” He’s also the kind of person who insists that his staff never say they “hate” a show or scene. At Berkeley Rep, you say, “I didn’t respond.” Respect and trust are “fragile virtues,” he says — difficult to build, easy to destroy. But if you work to build a whole culture of trust, the little tensions and tiffs that might escalate to derail another company can simply pass.

Reflecting on his career in an interview before rehearsal, Taccone, 67, adopts a different mode, as if he’s continually spurring his words, like a jockey bearing down on the finish line. Speech never comes out fast enough for his ideas. But he also has the disarming habit of frequently pausing to put himself in someone else’s point of view, imagining whether what holds true for him holds true for someone else.

Taccone says he and his company have always been the right size for each other. “It’s extremely rare that an individual’s desires and ambitions match an organization’s growth. It doesn’t happen, except once in a blue moon, and I caught the blue moon.

“I’ve never thought, ‘I’ve hit the ceiling. This is it.’ Never.”

He sees his career in the context of the whole regional theater movement — a movement born in the middle of the 20th century of the then-radical idea that not all theater need be New York-centric or commercial, that there exists “an engaged audience that wants to see complicated work.”

In the transition from founding Artistic Director Michael Leibert to Sharon Ott, in 1984, the theater moved “from being what I would call actor-centric to director-centric,” Taccone says. Ott “put the director at the heart of the conceptual aesthetic,” as opposed to focusing on a star or an ensemble. Designs became lavish. Shows bore “a particular movement, fashion, style, aesthetic imprint,” with visual vocabularies hailing from all over the world.

Taccone, who took over from Ott in 1997, says he took the theater in his own direction about 15 years ago. “I consciously set out to include the playwright at the center of the conceptual idea of what this theater can be and who it’s serving.”

Eventually that led to the creation of the Ground Floor, in 2012, Berkeley Rep’s in-house new play development center. It has a Summer Residency Lab each year that feels a bit like a sleep-away camp, but one attended by some of the most prestigious artists in the industry. Itamar Moses, Sarah Ruhl, Naomi Iizuka, Lauren Yee, Anna Deavere Smith and Daniel Handler are among current and past participants. The Ground Floor doesn’t require them to present anything publicly; they can use their time at Berkeley Rep however it serves them.

When Berkeley Rep’s board voted to continue funding the Ground Floor after a seed grant from Irvine Foundation ran out, “I was like, my work here is done. It was a great, great moment.” He calls it “one of the things I’m absolutely the most proud of.”

It meant that “one of the seminal, one of the most critical functions of Berkeley Rep was the sustenance and the creation and the nurturing and the development of new work. … It wasn’t just a one-off, like, ‘Here’s our new play in the season.’ ”

The Ground Floor has meant an influx of weird and wonderful artists whose needs and imaginations have stretched Berkeley Rep — puppet makers like Phantom Limb or musical theater makers like, this summer, the Bengsons. “One of the central questions of any organization that’s doing a lot of work is how can you expand the processes by which you make work? What’s the widest spectrum of artists that you can seek to support? In a rational way, because you can’t support everybody.”

To illustrate the point, he imagines a guy who makes theater in a cave. But even then he corrects himself; maybe there is a way Berkeley Rep could support that kind of art: “Workshops in the cave!”

On a more serious note, he says, “When I started, there was no such thing as a workshop. Now you don’t even consider doing something without a workshop.”

He counts two of his big mistakes as artistic director as resulting from the pre-workshop era. One year, “I programmed two new plays back to back, which I’m not going to name, because they both essentially failed … in large part because I didn’t workshop them. The idea wasn’t even around at that time. Looking back on it, both those plays had the potential to be really good. … In one case, the director came to me with this fantastic idea.” There would be 100 children, a journey with the audience into the theater from the loading dock, and a big forest. “It was a really good idea, and I kept saying, ‘Well, we can’t afford that, so what can we afford?’ We kept chopping down the idea, until we found something we could afford.

“Looking back on it, after a certain point, I should have said, ‘We can’t do your show anymore. This is not the show that you want to do. I love your idea; how can we create a structure to do your idea?’ ”

When Taccone steps down and Johanna Pfaelzer takes over, in September, he already has some projects lined up, with the Public Theater, South Coast Rep, one with Suzan-Lori Parks, as well as a TV pilot he’s trying to sell. “I’m trying not to completely fill up the time, because that is the way to just not do what I want to do.

“Some of it is simple things,” he adds. “It’s been 40 years since I’ve been really able to hang out.”

“Kiss My Aztec!”: Book by John Leguizamo and Tony Taccone. Music by Benjamin Velez. Lyrics by David Kamp, Benjamin Velez and John Leguizamo. Based on an original screenplay by John Leguizamo and Stephen Chbosky. Directed by Tony Taccone. Through July 14. $40-$115, subject to change. Berkeley Repertory Theatre, 2015 Addison St., Berkeley. 510-647-2949. www.berkeleyrep.org