Neil Simon co-wrote it, Burt Bachrach and Hal David composed the jaunty music, Vittoria De Sica directed it and Peter Sellers starred in it.

But when “After the Fox” came out in 1966, this sly farce about The State of the Cinema didn’t get a lot of love.

Simon and Sellers might have been at their peak — the first of a couple of creative and popular “peaks” for the famous playwright. And the cleverly-conceived and structured script had a few topical laughs and a lot of Italian and film business lampooning that played. But nobody wanted to see it.

Thankfully, this not-quite-romp has improved with age. We can appreciate a wholly-engaged Peter Sellers at his most animated, his wife Britt Ekland at her most coquettish and the great character ham Victor Mature coming out of retirement to send-up his entire tanned, grinning and “handsome” career.

And every single silliness-of-the-cinema and the chimeric delusions of the starstruck fans lands. Here’s a comedy that plays like a snapshot of Italy and Italian cinema in the ’60s, and an amusing sendup of stereotypes and the self-seriousness of art films of the era.

It’s not the best comedy of the era, the best Sellers comedy (Blake Edwards’ “The Party” gets my vote) of the time or Neil Simon at his wittiest. But it’s fun, especially if you’re old enough to remember Sellers or just now discovering the greatest screen comedian of his age.

Sellers dons an earnest, almost breathless Italian accent — not that different from his French one in the Inspector Clouseau movies — as Aldo Vanucci, aka “The Fox,” an honorable and famous thief seven months in prison for his last caper.

Having his prison wired — catering to his comforts — he’s content to finish his sentence. But his Mama (Lydia Brazzi) is unforgiving about his abandonment. And his younger sister (Ekland) is going wrong. She’s “on the streets,” his old cronies (Tino Buazzelli, Mac Ronay and Paolo Stoppa) tell Aldo. That moves The Fox to act.

“If only I could steal enough to beome an honest man!”

His services are needed to help crooks who stole gold bullion from Cairo get their haul ashore somewhere in Italy.

Dodging the carbineri (cops) and finding Gina “on the streets,” trying to become a movie star, inspires our Fox to come up with a plan. Making a movie would be a great cover for a caper, explaining away a crowd of crooks, winning the enthusiasm of the locals who won’t interfere because they all want to be “in the movie,” and even getting the cooperation from the cops.

All The Fox and his minions need is a cover-story/plot about the Cairo Gold, filmmaking gear (stolen from the set of a Biblican epic being directed by Vittorio De Sica) and a “name” for the cast.

Hollywood has-been Tony Powell (Victor Mature of “My Darling Clementine,” etc) is in town, not-quite defying age and Hollywood ageism, and not getting a lot of work in the process.

They have their cover story. They find a location — tiny Selvio, on the Neopolitan coast — and they have a date to shoot there. But delays at sea mean that great Italian auteur Federico Fabrizio (Sellers) will have to fake it until the bullion makes it…ashore.

Script? Plot?

“Een HERE (pointing to his head) ees my screept,” he bellows. “Een HERE (pointing to his heart) ees my plot!”

A Sellers this animated is always a delight to watch. But Mature marches in on those Groucho-length strides and vamps-up and double-takes his way to almost stealing the movie. There’s unmistakable delight in his eyes in every scene. And whatever Sellers thought was going on — he’d recruited De Sica, and then tried to get him fired — he seems to relish that he’s able to serve up comic big matzo balls to an aged screen veteran who’s in on the joke.

Mature? He’s making a Vitorrio De Sica movie, baby.

“I’ve got a NEW TRADEMARK,” ever-trenchcoated Tony tells his agent (Martin Balsam). “It’s called ACTING!”

Balsam sputters and spits as that agent, who keeps shouting “WHAT MOVIE?” as Fabrizzi/Vanucci talks up “my movie.”

“Neo-realism, what’s that,” Tony wants to know?

“NO MONEY!”

It also means a lot of sound-looping in post-production, with lots of non-English speakers dubbed by Robert Rietty, whose voice can be heard on many a 1960s film, including a few James Bond outings.

Akim Tamiroff is at his most comical as the blustering mastermind of the Cairo job.

And Ekland is the beneficiary of a movie star husband who helps her find the funny in a supporting part.

The screenplay, which Simon co-wrote the de Sica’s frequent collaborator Cesare Zavattini, has several ingenious bits of business above and beyond whatever gags Sellers cooked up (confusing his viewfinder lens for an ice cream cone is vintage Sellers).

Tamiroff’s underworld mug “Okra” stages his first meeting with The Fox at a busy tourist-friendly restaurant, where Vanucci chats and flirts with a beautiful woman (former Miss Italy Maria Grazia Buccella). She mouthes along to Okra’s negotiating words as the crook sits at an adjacent table. That’s a gag borrowed for the “Austin Powers” movies.

The prison escape scene is cleverly and efficiently set-up and handled.

And that visit to a De Sica film set — fake pyramids, fake John Huston as Moses, with Vanucci and his gang playing Hebrew “slaves” as they prepare to steal Cinecetta Studios’ production gear and a production truck — is cute. The grand old man of Italian neo-realism camps up his Great Director De Sica cameo, providing a model for the fake director Sellers will play as Fabrizzi — dashing, grand, grandiose and pretentious.

No, it’s not a laugh riot. But “After the Fox” — theme song performed by Graham Nash and The Hollies — isn’t just holding up well, it’s growing more adorably quaint with each passing year. It’s not the misfire it was judged to be upon release, and it’s not just pity or sympathetic grading-on-the-curve by Sellers fans saying so.

As Mature’s tanned Tony Powell puts it in the picture, “I’d rather get laughs than sympathy!”

Rating: TV-PG

Cast: Peter Sellers, Britt Ekland, Victor Mature, Martin Balsam, Lando Buzzanca, Vittorio de Sica and Akim Tamiroff

Credits: Directed by Vittorio De Sica, scripted by Cesare Zavattini. An MGM release on Tubi, Amazon, et al.

Running time: 1:43