Only when she opened her mouth and in her soft, quavering voice said, “It wasn’t just the music, it was everything about it. Just to know that if you go somewhere on a certain date, at a certain time, you’re just going to be blissed out for a few hours, that’s pretty nice … ” does her lunch companion remember that this elegant woman was Jerry Garcia’s sporadic lover for more than 20 years. “He was really just a great friend,” she said of the Grateful Dead’s leader and guru to millions of twirling, passionate fans. “Only, we did kick our relationship up a notch between marriages.”

Ms. Iaccaci grew up a long way from Haight-Asbury—the leafy lanes of Darien, Connecticut, to be precise. Her parents sent her to boarding school when she was 6. “That was the start of a bad taste in my mouth for boarding schools,” she said.

There would be 12 more boarding schools. “I’d run away, come home, and then they’d send me to another one,” she said of her parents. “They never really got it—until finally they decided that I was out of my mind, so they sent me to a mental institution in Connecticut—where, thankfully, I ran into a wonderful doctor who told them that there was nothing wrong with me, that I just wanted to be home, and just to send me to a school near home.”

At which point the Iaccacis decided to send their 17-year-old daughter to a school in Europe.

Ms. Iaccaci’s life from that point zig-zagged about the globe. At 18, she moved in with some girlfriends in the New York City and worked retail, then spent three years in Florence, where she worked as a model for Emilio Pucci. There were the occasional visits to the family compound in Ecuador: Ms. Iaccaci’s grandfather built railroads there. It was there, in the port city of Guayaquil, that she met her first husband, whom she married in 1964.

Cut to three years later: the summer of 1967, the so-called Summer of Love, and Ms. Iaccaci was a divorced, 27-year-old single mother of a 3-year-old son living in a $300 per month two-bedroom apartment on the Upper East Side.

But not for long: the sweet sounds of free love reached Ms. Iaccaci one day on a walk through—where else?—Central Park.

“It was right over there,” she said on a recent stroll, pointing to a path near the reservoir. “It was the most beautiful sound I’d ever heard.”

The sound was the strumming and harmonizing of two hippie dudes, who soon took up residence in her apartment. Soon enough so many like-minded folk were crashing on her floor, Ms. Iaccaci and her son Nicholas moved in with a woman named Ronny Keith, who lived on a houseboat/animal shelter off Staten Island. Ms. Keith was a herpetologist, and the boat’s residents included a caoti mundi, a boa constrictor and chimpanzee named Samantha.

It was there that Ms. Iaccaci met Cosmo, “my first hippie boyfriend.” In the fall of 1969, after attending Woodstock and her first Grateful Dead show, Ms. Iaccaci and Cosmo and Nicholas headed west.

“Cosmo and I refurbished a Volkswagen bus and we took off, waving goodbye to my mom at the Colony Club at Park Avenue and 62nd street,” said Ms. Iaccaci. “Oh, the look on her face! Just so horrified, like, ‘Oh, no.’”

Enter Laguna Beach, exit Cosmo. Up the coast in Santa Cruz, she met a new love, who was “one of the biggest producers of windowpane acid.”

“That didn’t last long—because it was no place to raise a child,” she said. “But I had a quick education in drugs. By the end of that relationship, I pretty much knew what every drug existing was, and I started going to Grateful Dead gigs.”

Ms. Iaccaci said she became close friends with the Grateful Dead “family” almost from the minute she met them.

“She was one of the people that came from New York,” said Jerilyn Lee Brandelius, who was the longtime love of Grateful Dead drummer Mickey Hart and wrote the Grateful Dead Family Album. “You could tell she was a bit of an aristocrat, but she really got into our reality pretty quickly. … The Grateful Dead attracted a large number of trust-fund babies. But Thayer was more than that—she’s interesting and intelligent and engaging.”

(Ms. Iaccaci insisted she never had a trust fund, but did allow that the family business, Aiken Industries, with real estate holdings and various businesses in Chicago and Ecuador, helped provide for her concert-going life; the farm she bought in Marin County in 1971—on which she raised llamas and other wildlife; and the apartment she currently owns on Lexington Avenue and 73rd Street.)

Her friendship with Jerry Garcia—who was married three times—did not become intimate until the “mid-70’s.”

“He was just always really nice to me, and I was always very nice to him,” she recalled.

Was it love?

“Oh, I’m sure I loved him. I don’t know if he was in love with me. I was awed by him. He was such an incredible musician. And a really interesting person, and funny! He read everything he could get his hands on.”

Up to Mr. Garcia’s death in 1995, Ms. Iaccaci attended 500 or so Dead shows. Among her rivals for Mr. Garcia’s attentions was Carolyn Adams, or “Mountain Girl,” a likewise lissome flower girl who would become Mr. Garcia’s second wife. Ms. Iaccaci said of Mountain Girl, “She was very protective of Jerry and she could be very mean … And she liked to keep Jerry nice and fat.”

(Reached by The Observer, Mountain Girl said of Ms. Iaccaci, “I really don’t have anything nice to say.”)

One of the best Dead shows, Ms. Iaccaci recalled, was a gig at the Winterland Ballroom right before the Dead took a two-year hiatus in 1974. “The last night of those gigs—the start of their hiatus—the Hells Angels came from all over the world,” she said. “Hundreds of them. And they were all backstage. And the band couldn’t even get off the stage. On a break, they couldn’t even get off! So I was taking orders, running back to the kitchen. That was just a wild night. You had to take a drop of acid if you went on the stage. There were so many blissed-out people, it was so much fun. I unfortunately had to baby-sit this girl I brought, who’d never taken acid before, but she wanted to go on the stage, so … I sat her on a trunk on the stage, and said, ‘Now you’ll be fine—just don’t move.’ And then she sees the Hells Angels, I guess she totally flipped out. I found her in a cabinet, in the kitchen, all curled up, poor dear, after the show was over. She’s forgiven me—but I told her not to move.”

Nevertheless, Ms. Iaccaci is a proponent of LSD.

“It just nails everything right on the head, doesn’t it?” she said. “It just makes everything really uncomplicated. It makes being a good honest person easier. It just simplifies things. It makes the things we worry about 99 percent of the time just hilarious.”

She said it wouldn’t be a bad thing at all if young people in America to start taking acid again. “Bring it back!” she said, noting, “There’s a lot more pressure now. It’s hard to get jobs, even if you go to college, it’s hard to make a living. Everything’s hard. Schools are awful, except the ones that cost $5 million a quarter.”

If Ms. Iaccaci were a young woman today, she said, she “wouldn’t want to bring kids into this world. The air pollution, all that we’re doing to good old mother earth. It’s just not good. … Greed’s taken over, money has trumped everything.”

Ms. Iaccaci’s idyll with the Dead couldn’t last forever, of course. She noticed some changes as early as the late 1970s, she said, around the time the Dead were recording Shakedown Street.

“I was around that whole scene, all the time day and night,” she said, “at the studio in San Rafael.” It was one of the periods when she was closest to Mr. Garcia, and she saw how drugs were getting in the way of the band’s productivity. “You don’t take acid and try to record an album,” she said. “You try to stay up all night, and all day, and all night, and all day, and all night … and try to sleep after that. I tried coke, I gave it a good try. Couldn’t do it.

“It’s insidious and awful,” she said of cocaine. “The minute that came on the scene, everything changed—not the exact minute, but it didn’t take long.”

Fortunately, for Ms. Iaccaci, her system wouldn’t put up with the hard stuff: “I’d have been dead a long time ago. I just couldn’t do the stuff that they were into.

“It’s a bad drug,” she continued. “I can’t believe that people your age haven’t figured it out by now. It’s just amazing, why would people still want to do it! We didn’t have any role models, to tell us it doesn’t work, bad news, don’t do it … God, so many people died.”

Ms. Iaccaci and Mr. Garcia survived the 70’s. But their relationship, which she said continually wavered between the platonic and the romantic, never approached the altar.

“I never thought I’d get married again, for starters,” she said. “But I did. I married one of the Pranksters, from Eugene, Oregon. Zonker. Did you ever read The Electric Kool-Aid Acid Test? Well, Zonker’s on the first page.”

Ms. Iaccaci and the “mighty handsome” Steven “Zonker” Lambrecht—who was the basis for Garry Trudeau’s cartoon strip Zonker character—wed in 1985. “I just fell for him from afar,” she said. “Especially because he looked a lot like Eric Clapton, who I was just so crazy about … We met, and we fell in love, and we got married.”

The couple divorced in 1994. “He’s dead now, he died of lupus,” noted Ms. Iaccaci. All along, she had continued attending Dead shows and keeping in touch with Mr. Garcia, who lived just down the road from her in Stinson Beach. She was backstage at Mr. Garcia’s last concerts at Madison Square Garden in 1994.

“It wasn’t a great life for him, the last few years,” she said. “Too much pressure, too many people relying on him. Too much bullshit. He didn’t really have fun. … No one left him in peace. He sort of got dragged in a lot of directions.”

In 1997, Ms. Iaccaci sold her ranch and moved to Montecito, California, to care for her dying mother. In 2000, she returned to New York.

“I always knew I’d come back here,” she said. Her three brothers are no longer living, but she said she’s grateful her son Nicholas, now 43 and a computer technician, lives nearby in New Hampshire.

She spends her days tending to a back injury and Oscar, her pet Chihuahua. Every so often she goes to a fancy dinner party.

“I would go to see music, but there’s nothing to see. It’s all so bad,” she said, adding that in her opinion even Mr. Clapton lost his mojo after giving up drugs.

But she doesn’t seem to have many regrets. She is well aware that, from the moment she hopped on that VW bus, she had a front-row seat at a moment when a music-loving, acid-dropping generation seemed truly poised to rip down all hate.

“I consider myself so fortunate to have been able to freely experience all that,” she said. “I have so many stories I can’t tell, that I’ll never tell, but it was just incredible.”

Asked if she was dating anyone, she replied, “Not at the moment.”