ATHENS — Every summer Greeks trade tips about island getaways the way New Yorkers gab about restaurants: Everyone has a favorite and, yes, where you go says a lot about you. That is what makes the British prime minister’s decision to visit one of the least-known islands in the vast Grecian archipelago so commendably quirky. The unflappable Boris Johnson and his wife, Carrie, might have chosen Mykonos like Elon Musk, but the two preferred to kick around Evia, the second-largest island in Greece after Crete.

While Mr. Johnson left some British tongues wagging by taking an extended vacation in Greece even as Britain reels from transportation chaos and a cost-of-living crisis, in Greece he charmed the locals almost the instant he landed. Apparently, he did not use a private plane. He bought his own groceries at an ordinary supermarket.  Then he showed up at a friend’s capacious but unpretentious villa and surprised islanders by visiting a remote beach with nary a sun umbrella or VIP beach bar in sight.

Newspapers in Greece reported that Mr. Johnson even rented his own car to putter about the island on his own, with only a minimal security detail. The owner of the rental company, wearing canary yellow pants,  handed the British premier — wearing navy blue shorts — a timely book titled “Greece in Poetry.” 

That did it for me. I wanted to see some of this island’s allure for myself. If I ran into the British premier while doing so, it could only be a plus. The history of Evia is itself a draw. The name in Greek, Εὔβοια, stems from ευ, like the “e” in euphoria, and βους means ox, so in antiquity Evia was the Island of the Blissful Cow. Goats are mostly what I saw, but they seemed reasonably content.

Mr. Johnson fashioned himself a perch at Karystos, a beachfront town in the southern reaches of Evia where there is a Venetian fortress that dates from the 13th century. I focused on the area around Chalcis, or Chalkida, which one can drive to via a short bridge from the Greek mainland. Chalcis is included in the legendary “Catalogue of Ships” in the second book of Homer’s “Iliad”; Evia was a staging ground for the siege of Troy. According to some sources, King Agamemnon’s fleet was held back by inclement weather on the Euboean shore before it could sail across the Aegean.

That Chalcis is home to the oldest Jewish community in Europe surprised me less than its spectacular and virtually unknown back country. Vertiginous peaks and switchback roads to match, untamed cliffs plunging to the infinite sea and hidden villages almost bafflingly Alpine in character — but with al fresco souvlaki spots reminding you where you are — Evia is an island whose jagged contours smack you like a landscape out of Tolkien’s Middle-earth. 

Its rugged north side resembles Italy’s Amalfi coast in spots, minus the crowds. The best beaches, whether long and open to the Aegean Sea or quiet coves, can be reached only via frequently tortuous roads. A fire truck overtook my car at one point and I soon saw why: off to the side of one particularly hairy bend a vehicle had flipped over. 

Hot springs abound; the most renowned are in the north at Adipsos, where Aristotle is said to have journeyed from his Peripatetic School in Athens to soak in the healing waters. In antiquity Evia vied with Athens for regional supremacy. Euboea lost out to Athena and receded to the footnotes of history, but if these days seclusion and fresh air trump crowds and smog, it might be time to reassess that particular historical scorecard. 

The island is a mystery to this correspondent. With only a day to explore, can one obtain any more than a periscopic glimpse? Yet to zigzag around Evia’s tangle of country roads and mix briefly with the down-to-earth locals is also to peer into the unfairly maligned character of Boris Johnson — on Monday, the Times of London reported that according to polling, Conservative voters have “sellers’ remorse” over Mr. Johnson’s ousting “and would prefer him as prime minister over the two rivals vying to be his successor.” 

Mr. Johnson’s unscripted Grecian sojourn may have pushed him off of Fleet Street’s front pages, but signs indicate he may have been less absent than simply refueling, and is not yet down for the count.