To try to stay on topic, here's a story that, while a bit newer than the 60s, is on-topic & some guys may even relate to it.
Up until the early 80s, Central Ave in Phoenix, Az. was the place to be. When I was a rookie, I was sitting on a side street one Saturday night, just waiting for some guys to "light 'em off".
Sure enough, inside of 20 minutes 2 guys square off at an intersection about 4 blocks from me. Since this was nighttime they couldn't see me, but I could hear their engines revving, each one trying to coax the other into jumping first. When the light went green both cars took off, the '66 Goat pulling the Camaro by a fair amount. As they passed me, I followed in, going after the Goat. The driver tried swerving a bit in & out of the traffic he had caught up to, but now that he was forced to slow down I easily stayed with him. He finally pulled into a parking lot, jumps out of the car & starts screaming: "Honest, Officer my brakes failed & I couldn't slow the car down!"
Yeah, right....
I went up to his car, stepped on the brake pedal numerous times & as expected his brakes were fine-he was screwed up! I told him he was flat-out he was lying & that I saw his whole "race" from the start. He kind of apologized and after receiving about 5 tickets he was allowed to go.
Being an old-time streetracer in a place where it was a daily occurence has its advantages. While I never wrote alot of "drag racing" tickets in my day, when I retired I was looking over some old paperwork & realized I had a 100% conviction rate--bad for the racers,but I think it did show I knew a race when I saw one........