Remember when you would see a movie where someone's "driving" & you would say, "Look at Him Shimmying that Steerig wheel back & forth like he's driving, he'd be all over the road." Well it turns out they got it from the old Model A days when, yeah, people drove like that. Just like TV
You'll notice that all the driving in movies has the back and forth turning of the wheel in the through the windshield shots. This goes back to the earliest days of audience surveys by motion picture makers. If the wheel wasn't being worked the audience did not belive the car was moving. If the elevator floor indicator didn't show the arrow pointing out the floor numbers the audience thought the folks were getting out on the same floor they got on. One of the funny little things about pictures that make them so wonderful.
One the other hand, if your Model A is doing that it needs the box adjusted properly and same for tie rod ends and alignment. Still doing it? A rebuild of some or all sterring components is in order. NO new or rebuilt correctly done car should have more than 1" in steering wheel slop.
I remember my mom's 34' Chevy 4-door with knee action shocks. It shimmied on RR tracks, bumps, and dips. Rode in that thing from central Illinois to Portland and back. What fun.
Mine use to drive that way till I got a new Flaming River box. New product Made in America. Problem solved.