“He didn’t like my work, apparently,” Ziegler once said of this one-man bottleneck — a makeup editor named Carmine Peppe who aimed to exercise control over which cartoons to hold. But what Peppe didn’t realize was that Ziegler represented a new wave of New Yorker cartoonists, and that this tide would not be denied.

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“It turned out that Carmine thought that if they printed my stuff, it would be the end of the magazine and that it would just destroy The New Yorker as we know it. Which it did, apparently,” Ziegler said with a laugh in Richard Gehr’s 2014 book of profiles, “I Only Read It for the Cartoons: The New Yorker’s Most Brilliantly Twisted Artists.”

Under then-cartoon editor Lee Lorenz (who overrode Peppe), Ziegler would indeed help usher in a new class of New Yorker cartoonists that included Roz Chast and Charles Barsotti — talents with distinctly individual comic voices. Which is why cartoonist Michael Maslin’s website Inkspill has called Ziegler “the godfather of contemporary New Yorker cartoonists.”

“He brought a new sensibility to the New Yorker — something more surreal and unexpected,” Chast tells The Post’s Comic Riffs of Ziegler. “He was a true original voice.”

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Ziegler, who died last week in Kansas City, Kan., at age 74, would go on to publish more than 1,600 cartoons in the New Yorker. “That puts him in the top five all-time for the magazine,” cartoon editor Bob Mankoff, who will leave his magazine post at month’s end, says of Ziegler’s output, which was recently donated to the Ohio State University’s Billy Ireland Cartoon Library and Museum.

As Ziegler evolved, his gifts became so subtly brilliant — his sense of economy, his deft gag structures, his precise timing — that it can be harder in hindsight to appreciate just how influential he was becoming in the ’80s and ’90s.

“Jack’s cartoons were groundbreaking,” says Liza Donnelly, a veteran New Yorker cartoonist and “CBS This Morning” contributor. “They were funny, often odd and bizarre — you could see Jack’s world view in his cartoons.

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“They weren’t about a ‘joke,’ necessarily, even though they were funny,” she continues. “They were about something else.”

Ziegler could do boardroom and barroom humor with the best of ’em — stock settings for the single-panel cartoonist. Yet he had a fondness for finding sly laughs in hamburgers and toasters; in creatures wild and dogs domestic; in marriages beginning and dissolving; and in out-of-water scenarios for Superman and the Lone Ranger.

His cartoons “could range from inspired absurdity to trenchant satire, all accomplished with a superb artistry that was never satisfied with the boilerplate cartoon iconography that lesser cartoonists accept,” says Mankoff, who calls Ziegler his favorite cartoonist.

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“And I’m sure I’m not alone,” adds Mankoff (who notes that seven New Yorker cartoonists have died in the past year).

The Brooklyn-born Ziegler grew up on the newspaper funnies and EC Comics before discovering the New Yorker through boyhood friend Brian McConnachie, who became an Emmy-winning writer for “SCTV Network,” “Saturday Night Live” and National Lampoon. It was only in the early ’70s, after non-artist McConnachie got paid for producing the satiric “Worst Cartoons in the World,” that Ziegler began to seriously pursue creating some of the better cartoons in the world. After deciding San Francisco’s alt-comix scene wasn’t a good fit for his skills, he moved back East with his young family in tow, got a tip from Lampoon legend Michael O’Donoghue to make his drawings less realistic to make them funnier, and by 1973 sold a New Yorker cartoon idea that was illustrated by the great Charles Addams.

Lorenz soon offered Ziegler a New Yorker contract — something he extended to promising talents about four times a decade. Ziegler never looked back, following what made him laugh rather than try to please an abstract magazine audience. He would sit to doodle, and then his pen would trigger his spring-loaded comic mind.

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Meanwhile, Ziegler in person was as approachable as the bespectacled, bulbous-nosed people in his cartoons.

“Jack was a great cartoonist … and was also a great friend: funny and smart and kind and a generous laugher at other people’s jokes,” Chast says.

“Jack was a sweetie, a softie, a generous man. He was thoughtful — not the write-thank-you-notes brand of thoughtful, but the kind that came from his soul. From the first time I met him, I felt like he was the big brother I never had,” says Donnelly, who along with Maslin, her husband, and a band of other New Yorker cartoonists hung out with Ziegler often.

“As a young cartoonist just arriving in New York City [circa 1980], I studied his book ‘Hamburger Madness’ inside out,” Donnelly says. “I searched for his method. What I found was an attitude that said: This art form is to be manipulated, played with to your needs. And don’t forget, it’s fun.

“To me, his cartoons said: This world is wacky — enjoy it.”

“His cartoons, as the man himself,” Donnelly says, “were a wonderful mixture of fun and deep.”