Wendy Kozma, 58, a real-estate agent living in West Bloomfield, Mich., on her 1966 Ford Mustang, as told to A.J. Baime.

I was the youngest of three kids, and my parents promised us kids that if we worked and we could pay for our own gas and insurance, they would help us get a used car when we turned 16.

When I turned 16, my father asked me what I was thinking. “I really want a Mustang, Dad,” I told him.

When Ford introduced the Mustang in April 1964, it became the most successful consumer car ever launched up to that time in terms of sales figures. Wendy Kozma in her first-generation Mustang.

At the time, the Mustang II of the 1970s was the model I was thinking of. He said, “That’s not a real Mustang.” He thought a Mustang from the first generation of the 1960s would be cooler and would hold its value.

We started searching in newspapers, but the cars we found in Michigan were rust buckets because of the winters and the salt on the roads. That fall and winter came and went, and in the spring, I went on a trip to Mexico with my high school marching band. When I came home on the bus from the airport, I was excited because this was my first time on an airplane and my first time away from home without my parents. When we got to the high school, my parents were there in the parking lot with this car.

They had found it in Tennessee and had gone there to get it. They paid $1,250 for the car and my father had driven it home. It was a very emotional day when they gave it to me. The car was 13 years old, with its original 200-cubic-inch, 120-horsepower, six-cylinder engine. According to the paperwork, it was manufactured in Michigan, the state where we lived, but originally sold in 1966 at a dealership in Macon, Ga. Ford debuted the Mustang as a 1964½ model, so this car was from the first couple years of production.

The restored 1966 Mustang’s interior. This car came off the assembly line on July 26, 1966. ‘She purrs like a kitten,’ Ms. Kozma says.

Part of the Mustang’s allure has always been its galloping-horse logo, seen here set into the car’s grille.

My father worked as a supervisor at Ford’s Michigan Assembly Plant in Wayne. He loved all things that went fast—motorcycles, go-karts, dirt bikes. One month after I got my Mustang, he passed away in a motorcycle accident. He was 41 years old. My mom was 39. I was 16. It was a very hard time for our family, and this car became even more important to me, because it was like he had left a piece of himself behind, for me.

Through the years, I moved many times. The Mustang always came with me. During the 1980s, my brother did some restoration on the car and repainted it yellow. For a while, the car sat on the back burner and didn’t run at all. For my 50th birthday, however, my husband, John Kozma, vowed to restore the car from top to bottom for me. A shop called Motor City Solutions in Taylor, Mich., did the work. They repainted it to its original color, Sauterne Gold.

When it was time to pick up the car, my mother and I went together, and when we saw it, my mom just broke down. It looked just like it did on that day when I first saw it in my high school parking lot in 1979.

The 1966 Mustang’s 200-cubic-inch, 120-horsepower, six-cylinder engine.

Photo: Erin Kirkland for The Wall Street Journal

I still have the original title application from 1979 with my father’s signature on it—Ray W. Dodd—and other paperwork showing the car’s original birthday when it rolled off the assembly line, July 26, 1966.

These days we drive this car for pleasure and it purrs like a kitten. We take it to car shows, and we have driven it in the Woodward Dream Cruise in greater Detroit, billed as “the world’s biggest cruise.” People are always surprised when I tell them that I still have my first car. When I start it up, it sounds exactly as it did the first day I started it up in 1979.

Ms. Kozma’s father died when she was a teenager, shortly after she received this Mustang as a gift from her parents. Here she is with her mother, Janice Dodd.