As it happens I was at the particular edition of the Elsinore Grand Prix they filmed for the movie although not competing myself. In On Any Sunday there is an overhead sequence shot from a helicopter before the start of the race and if you look real close I was down in the crowd with my Super 8 movie camera filming assorted stuff including some helicopter flying low. I was also snapping still pictures with my little Kodak Instamatic camera. As we all looked up at the low flying copter someone remarked "They're filming some sort of movie about the race, I guess because Steve McQueen is racing in it." You can't actually see me in the crowd but I was there. Big deal, I know.
I wandered up to near the front of the starting field of bikes and not too far back from the front row stood Steve McQueen by his Husqvarna. I've never been much on celebrity fascination but it was fun to see one of the biggest Hollywood stars of the time getting ready to race a dirt bike.
Later, McQueen was sitting quietly on his bike, collecting his pre-race thoughts no doubt, and folks were mostly leaving him alone. A woman walked up with a pen and paper and asked for an autograph. I was close enough to hear him say firmly but not impolitely "Not now, catch me after the race."
A bit later a little girl walked up, she was perhaps 7 years old, and offered up a pen and paper and asked for an autograph. McQueen looked down at her and flashed his million dollar smile, "Honey, for you, sure!" He picked up the little girl and sat her on the red tank of the Husky and put his arms around her and autographed her piece of paper. He chatted with her a bit but I couldn't hear what was said. I always thought that was a classy thing to do. No doubt the little girl had been put up to it by an adult but McQueen was too much a gentleman to disappoint a child.