Long Island’s spanking new $20 million tourism center — with its replica lighthouse, a whale rising out of a cement pond and celebrity walkway — owes its life to a clunker of a pickup truck that got stuck in 2006 at the rundown rest stop near LIE exit 51.

It also had a lot to do with the clunker’s driver: Gov. Andrew M. Cuomo.

Cuomo recounted the breakdown to more than 500 people at the Suffolk Democrats’ fall dinner last week. It was a glimpse into how state policy can turn sometimes on the personal, not political.

As the governor recalled, he was driving a Chevy El Camino — an eBay purchase he labeled “a total mistake” — so he could fix it with his brother Chris, a CNN anchor, at his South Fork home. “I’m going down the expressway and boom it dies,” said Cuomo.

He called his brother for a ride, but while waiting Cuomo tried to nap. He got a knock at his window and a young lady asked, “Would you like to go out tonight?” Since he was already “technically out” and the car wasn’t running, he said, “I don’t have any way to go.” When she said it didn’t matter, he declined her offer.

Later came a second knock by a man who asked, “You need something to stay up or . . . help you go down or . . . forget your troubles?” Before long, another man knocked, also asking if Cuomo “wanted to go out?” Again, he demurred.

Cuomo said that after he got to Albany as governor in 2011, he began to ask around. “What’s wrong with this rest area? It’s wild.” There were not only prostitutes and drug pushers, but noisy trucks “that stink like hell with diesel smoke,” Cuomo said. And without restrooms, drivers do “what happens naturally” in the bushes.

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Cuomo recalled that aides warned, “You can’t do anything there, the local community is dead set against anything . . . somebody tried 15 years ago . . . lost office and moved to New Jersey,” though no one could identify the exiled pol. Another aide called it “political suicide.”

What the governor did not mention in his narrative is that in August 2015, his Transportation Department moved ahead with a request for proposals and cut down trees without telling state or local officials, stirring community anger not seen since Gov. George Pataki had a similar plan.

“I won’t mention any names,” said Cuomo, but immediately identified Huntington Town Supervisor Frank Petrone, who told him “I’m on the ground you’re in the sky . . . you can’t do this.” Cuomo recalled telling him, “In the next election are you going to say ‘Hi, I’m Frank Petrone, I believe we should have additional prostitution and drug deals?’ ”

Petrone later said he advised Cuomo: “ ‘Talk to their community and deal with their concerns. There’s a lot of history . . .’ And he took the bull by the horns.”

After repeated hearings and meetings, Cuomo agreed to close the westbound rest stop, and banned trucks from the new tourism center, which is complete with state and county police outposts.

Even Republican Assemb. Andrew Raia of East Northport said Cuomo showed an unusual “willingness to bend” on the issue.

“At first we went bananas because the real problem was always the trucks,” said Raia. “But I have to give him credit he was the first of the five governors involved with the issue who listened . . . He even called me once during dinner.”

During construction, Cuomo remained involved, changing the color of restroom tiles on one visit. “I didn’t like the color of the tiles,” which he “thought clashed with the hallways.”

“I know the skepticism,” said Cuomo, “I know people think we in government are never going to do anything. We make it worse.” But he told the crowd the project was done on time and under budget. “This is a place you are going to be proud of,” he said.

The El Camino was not so lucky. It remained garaged until the brothers sold it a few years later.