Steve McQueen in His Jaguar XKSS
Trailing Steve McQueen was Dominis' first Hollywood gig. "I liked the movies, but I didn't know who the stars were; I was not a movie buff," Dominis, now 88, tells LIFE.com. But he got the assignment because he and McQueen shared one vital passion point. "When I was living in Hong Kong I had a sports car and I raced it," Dominis says. "And I knew that Steve McQueen had a racing car. I rented one anticipating that we might do something with them. He was in a motorcycle race out in the desert, so I went out there in my car and met him, and I say, 'You wanna try my car?'" Later the two of them would zip around Los Angeles, including Sunset Boulevard (pictured). "We went pretty fast — I mean, as fast as you can safely go without getting arrested — and we'd ride and then stop and trade cars. He liked that, and I knew he liked it. I guess that was the first thing that softened him."