It is 9 a.m., and John Gavin, 52, the actor-turned-diplomat and current U.S. Ambassador to Mexico, prepares to head for the office. For the 20-minute trip from the ambassador's residence in the exclusive Lomas suburb to the embassy in downtown Mexico City, he travels by chauffeured limo, a long, bulletproof Lincoln complete with a bodyguard riding shotgun. Another carload of armed security agents trails closely behind—extraordinary precautions for an American diplomat even in these terrorist-ridden times. And this day Gavin's workload will be even heavier and more delicate than usual. He is laboring to pave the way for his boss, Ronald Reagan, to hold a sensitive summit conference in La Paz with Mexico's President Miguel de la Madrid Hurtado, whom Gavin will accompany to the meeting in the Presidential 727.

Meanwhile, back inside the walled compound of the official residence, Gavin's wife, singer-actress Constance Towers, 52, has her hands full with a different set of problems. She is conferring with the household staff on the menu for a reception for 350 guests that afternoon and is understandably tired, having flown back to Mexico City from Los Angeles at 2 a.m. The previous day she had put in 12 hours in front of the camera portraying the matriarch Clarissa McCandless in the CBS daytime soap Capitol. Her shooting schedule requires such 3,084-mile hops to L.A. and back twice a month or more, and juggling her fictive and real political roles has its hazards. Once she had to dress for a diplomatic reception in an airport ladies' room—and, she adds, "got stuck in a stall."

As the nearly three-hour meeting that took place last week between Presidents Reagan and de la Madrid underscored, Mexico is of pivotal importance to U.S. diplomacy, all the more because of the military action taking place just south of Mexico's border. The 1,181-member embassy is America's third largest, and Mexico's common border with the U.S. makes it a hotter spot than most. "If you're not attacked at least once a month," Reagan warned Gavin when he named him, "I'll feel you aren't doing your job."

He needn't have worried. When the appointment was announced in 1981, many Mexicans hooted that Gavin's only qualification was his longtime friendship with Reagan. The fact that he was then earnestly plugging Bacardi rum on a Mexican TV commercial while his 1978 horror movie, Jennifer, was playing Mexico City theaters did nothing for his stature in the country.

But from all indications, Gavin has grown, even thrived, in his sensitive posting. "I've lived here through 11 American ambassadors," says U.S. businessman Victor Agather, "and Gavin is by far the best." Adds Connie, loyally, "Jack was far better prepared than most people realized. His mother was born in Mexico and he has a degree in the economic history of Latin America from Stanford. He's done work over the years for the Organization of American States. He has had business interests, developing property in Central America and Mexico, and he speaks fluent Spanish."

In two years the Gavins have become Mexico City's glamour couple, and they take Connie's schizophrenic life-style in stride. "We decided when we were married that we'd never get in the way of each other's career," she explains. When she starred in 1977's hit Broadway revival of The King and I, he did the long commuting from their West Coast home. "Now it's my turn," she says. "Sure, I miss not seeing him every day, but he loves his job so much and we talk on the phone almost daily, sometimes several times a day."

In his student days in Ojai, Calif. (where he was Villanova Prep's left end and National Security Adviser William Clark was right end), Gavin actually aimed at a career in diplomacy. But after service as a Navy intelligence officer during the Korean War, he drifted into acting at a friend's casual suggestion. Hailed as a second Rock Hudson, he played opposite such leading ladies as Susan Hayward (Back Street), Janet Leigh (Psycho) and Sophia Loren in the 1980 TV story of her life. ("Kissing Sophia was great," he says with a grin. "Lifting her was something else.") His career was also sprinkled with less memorable films, such as Tammy Tell Me True. "I may have had some banal roles," he admits, "but they were never embarrassing."

Gavin, whose mother, Delia Pablos Golenor, is a member of a prominent ranching family in Sonora who became an L.A. socialite, traveled in the poshest circles, and it was at a party in 1957 that his godfather, songwriter Jimmy McHugh, introduced him to Connie. They met again years later, when both were divorced parents with two children. (His are Cristina, 23, a Stanford grad, and Maria, 20, who attended the Colegio de Mexico in Mexico City; hers are Michael, 23, a UCLA premed student, and Maureen, 20, who works in a Beverly Hills clothing shop.) Since their marriage nine years ago they have smoothly melded their families, careers and personalities. While he is intense and fastidious—his children rag him about his habit of straightening cutlery at the table—she remains steadfastly cheerful and calm.

Born in Whitefish, Mont, to a businessman and a housewife, Towers had to overcome crippling polio as a teenager before she carved out a sparkling career in musical theater (Show Boat, The Sound of Music) and films (The Horse Soldiers with John Wayne). Still, she admits that her role as an ambassador's wife has brought unexpected challenges. On arrival in Mexico City she found the 20-room ambassador's residence "in terrible shape. There was mix-match furniture from a dozen previous ambassadors. The roof needed repairing, the walls were dirty." Enlisting Mexican artisans and a hot young L.A. decorator, Tim Morrison, she launched a restoration. The job is far from finished, but already borrowed art worth perhaps $2 million—including an Andrew Wyeth and a Georgia O'Keeffe—grace the freshly painted off-white walls.

About a year into her husband's term, Connie was offered the Capitol role. "We talked it over," she says, "and Jack didn't object." But, mindful of the flap over his TV and movie appearances, there was one stipulation: only "good person" roles. "I feel a deep responsibility for my husband's position," she explained in an interview, "and I simply could not play a manipulative, evil person and wind up having the people of Mexico see the ambassador's wife being someone they couldn't believe in." Sometimes, when shooting keeps her from an important function, Gavin's mother flies down to fill in as hostess. "She just sparkles," Connie says.

Ironically, it is he—not she—who has been criticized in the press for absences from his post ("more than 100 days" in his first year, according to a leftist Mexican columnist). "Sure I travel," Gavin retorts. "I went to Washington to negotiate a $1 billion prepayment to Mexico on its oil revenues to help it out of its financial crisis. I was also negotiating tuna-fishing disputes, immigration policies, trade conflicts." Lately, although his occasional preachiness rankles some Mexican pols, Gavin's firmness, macho manners and good looks appear to be winning converts to his side. Watching the couple working the crowd at a reception, smiling, relaxed and pressing flesh, one local observer quipped: "Even Ronnie and Nancy could take lessons."

Ultimately, of course, ambassadors serve at the pleasure of their President. While Washington's confidence in its envoy to Mexico seems solid, what will he do when the appointment has run its course? "I'm not going back to acting," Gavin vows, "and I'm not going to seek elective office." Appointive office? "Maybe, though I wouldn't mind going back to being a businessman. But first I intend to finish what I've started here in Mexico." It is said with the conviction of one who expects a long run.