This is because your cones (colour-specific 'pixels' in your retina) cluster around your fovea (high-resolution area around the center of focus) while the rods (black-and-white, bigger, dumber, but much more sensitive and therefore faster-responding 'pixels') fill the rest of your visual field. Rods respond fast enough to see the flicker but cones don't.
You might also notice in light that's almost too dim to see, you can see things better if you look a bit to the side of them, for the same reason.
For me, it's also noticeable when my eyes are sweeping from one object to another. Like you should be doing when driving. I guess that's somewhat peripheral, but not entirely.
Find a Cadillac Escalade with the vertical LED lights, and give it a try.
What's a good way to capture this on video? Or to measure the frequency?
That's a different thing. Your eyes automatically filter out the blurry signal during a saccade (ie. while they're doing a fast pan from one location to another.)
Rapidly strobing lights (eg. LEDs being PWM'd) mess with this process and cause you to perceive the intermediate images as your eye moves, leading to some weird visual effects. This was a big thing in the early days of DMD projectors, where they projected sequential red/green/blue frames, and while it looked great when you stared at it, any time your eyes moved the whole image strobed with overlaid RGB fields. (more info: https://www.prodigitalweb.com/rainbow-effect/)
