The question detail added since I wrote this pretty much eliminates my early theories. I've now split the original answer out below what is still mainly guesswork.
If you examine this sequence frame by frame, you'll see these stripes appear & disappear exactly every other frame. That makes me think it is not in the digital transfer or any subsequent processing, but in the original footage.
I cannot think of any transfer process that would divide these frames so precisely.
I have looked at the current BluRay release of this as well as the gif & excerpt posted by the OP & it matches exactly. The BluRay is at 23.98 fps, which is a bit of a kludge to map to the old US/Japanese NTSC video system Don't ask;) , but is close enough to the original 24fps that inter-frame aberration should happen infrequently.
I don't think it could be any kind of physical 'shake' of the vehicle or lights - because the chances of that syncing perfectly to frame rate would be astronomically small.
The only conclusion I can draw at the moment is that there may have been something in the shutter/gate mechanism that presented itself slightly differently on alternate frames. I'm not really sure how this may happen. I've discovered that the camera used, a Mitchell BNCR, may have had an optical splitter fitted, which would present light to the film & to an eyepiece for the cameraman.
Quite how this functioned I don't have the expertise [or the Google-fu] to know for sure.
There are a couple ways this may have been achieved.
There may have been a moving pentaprism design somewhat akin to a [D]SLR ([digital]single lens reflex) camera - alternating between sending light to the film & to the camera op. To my admittedly limited knowledge, there was a 'movie' version of this which rotated to send the light in alternating directions - to film, then to the camera op, 24 times a second.
It may have used a beam splitter, the science of which hurts my brain;) The simplest version of this seems to be the pellicle mirror. These were first introduced as early as 1938, but even to this day they are not popular in 'stills' cameras. The pentaprism remained the most common structure until quite recently when mirrorless cameras started to come to the fore. These use a digital screen as a viewfinder, eliminating the need for a separate optical path.
See When recording on film, how does the crew see the footage? more more info on modern video taps.
Original answer below.
The streaking is an aspect of the lens flare you can see through most of the shot - light being reflected inside the lens and camera body itself. It's at its 'worst' when the headlights are pointing more directly at the lens.
The flicker I can only guess is because they're LED headlights. You can get completely flicker-free LEDs, for such as video lighting or anywhere near fast-moving machinery [drills, power saws etc] where the flicker would be annoying or outright dangerous, but usually LED brightness is determined by how long the light remains on compared to off. This is known as PWM [pulse width modulation].
I am no electronics expert, so I've never fully investigated why they do it this way when it's possible not to, but my first thought would be 'it's cheaper'… as is usually the case.
This gives an explanation - https://www.analog.com/en/design-notes/lowpower-pwm-output-controls-led-brightness.html Don't ask me about anything you don't understand ;)