Baja California is the long tail that hangs along the southwestern rump of North America. The Sea of Cortes — on which I doubt stout Cortes ever gazed, with or without Keats’s “wild surmise” — is the sliver of sheltered sea that separates Baja from the heartland of Mexico. It is the home of what used to be innumerable fish, shrimp and lobster. In the winter months, a congress of whales meets, mates and proliferates in the warm winter water. Sightseeing Captain Ahabs come to observe their sleek, improbable thrash.

We first went to Cabo San Lucas thanks to a Midwestern frozen-chicken billionaire. We never actually met Don Tyson, but he was a friend of an Arkansas professor of creative writing who occasionally flew me in to electrify his students. Don’s latest spare-time ambition was to be the Arkansan Vladimir Nabokov. My friend was showing him how.

Don’s greatest ambition, however, was to catch the biggest marlin in the world. When the fish were in fat supply, he flew down in his private jet and raced out to sea. His thrill of thrills was to come back into harbour with a huge trophy slung astern. Don had a big house and two guesthouses, convenient to San Lucas harbour. Cabo San Lucas is Baja’s answer to Key West: the last stop before you fall off the continent.

A beat-up taxi took us from San Jose airstrip through the low scrub of the peninsula, down a long dirt road to the gated compound where Don’s third-best house was ours for the week. One of his cars, we had been promised, would be at our disposal. Porsche or Lamborghini? It was a rusty, stick-shift Ford station wagon with a door that had to be slammed and held shut if it was going to stay that way. Only very stupid ricos drove look-at-me cars into and out of Cabo in the 1980s. The local bandits followed the Mercedes of likely marks back from San Lucas after their lobster dinners. When they got out to unlock the gates to their fancy homes, the bandits came on in. In Baja Cali- fornia, nobody could hear you scream.

The morning after our arrival, Captain Osvaldo rang our bell. When would we like to go marlin fishing? Mr Tyson’s ocean-going powerboat was ready and waiting. Chance of a lifetime.

“Mañana? A las diez, al puerto San Lucas.” Deal. We reported at 10 to the little harbour, where Captain Osvaldo — bearded like Tintin’s Captain Haddock — was preparing several strings of hooks. These were to catch the mackerel that would serve as bait for the Big Guy, like the one Papa Hemingway’s Old Man wrestled with to prove that he still had cojones.

The boat sped with this’ll-show-’em speed past the lolling sea lions who watched us from the rocks. After we slowed, Captain Osvaldo came down from the bridge and trailed his lines from the stern. Almost immediately he was pulling them up again, flagged with the bluish-silver small fry that brought the gulls clustering behind and above us. The haul was posted, bait in waiting, in a tub in the stern.

Osvaldo explained how, once we had a bite, he would strap us into the belted armchairs facing the stern, and the fun would begin. Except it never did. We sat studiously in the silent boat, rising and falling, rising and falling. Once or twice, urgent gulls swung towards some distant boat. Other boats followed, and so did we, for hours, and hours. The sea lions watched us back into harbour. They too hadn’t done anything worth a damn all day. But they still had their dignity.

The next day, Captain Osvaldo knocked at our door, but we did not feel the vocation. That was us and sport fishing.

In those days, Cabo San Lucas had just two big hotels, and very nice they were, but that was it. The town itself had one somewhat paved main street. Dirt side roads led to tar-paper shanties you were ashamed to look at. There was little to buy and less to do, aside from eating fresh lobster and drinking tequila (we preferred Dos Equis, the local beer).

Until the 1990s boom, Baja was the sterile, sun-dried appendix of Mexico that the gringos didn’t bother to grab while they were remembering the Alamo. Mariachis didn’t play. A scruffy desert with a stubble of scrub, only the bristling yuccas gave it the thumbs up.

THAT WAS then. Now the gringos have arrived in force, armed not with Colts and Winchesters, but with golf clubs. Swinging their way down the peninsula, they have left it cratered with sand traps and greener than nature intended. Gigantic Hiltons and Sheratons are flanked by Jack Nicklaus-designed championship courses and the palmy amenities that go with them. The One&Only Palmilla, where I had been invited to cast a critical eye over its $80m refit, is the latest in a sumptuous series.

AT THE airport, we were met by a liveried Jeep — a promising start, and it got better. To keep the crowing to a decorous caw or two, let me say only that we had the best room we have ever had in a sun-seeking lifetime: huge bed, high ceiling, House & Garden decor, marble floor, bedroom/sitting room and a bathroom as big as the Ritz. Even our terrace came in two stages: an undercover ottoman and, beyond it, outdoor loungers with a view of the sea across the sprinkled lawn.