Did you not mention what the flicker rate was? < 10Hz ? > 30Hz? only on activation of brake lights?
There are at least three question/answers.
- Why does it flicker? (=PWM effect)
- Why do we perceive it off center more as flicker (human optics)
- Why do we perceive it more as modulated streaks on center when the car is moving? (human optics)
Now some details:
Let me address some general common issues;
1) Cadillac LED brake lights "were" notorious for causing eye flicker response.
The cause was a PWM rate was high enough to be unnoticed when direct viewing the rear end of a stationary car, but noticeble when the car is moving while braking and more so, from your peripheral vision. Both conditions increase the human eye-brain sensitivity to flicker. This is well documented.
**added*
This graph shows the eye distribution of Rods & Cones. Rods, used for night vision, have a broader Field of View (FOV) from center than cones. Rods are also more sensitive but active only at low ambient light levels. This accounts for the increased sensitivity of flicker on peripheral vision at night.

2) When the eyes move, the human vision is more accute to the flicker while they are in the peripheral. Once the eyes view the car directly while it is slowing down at night, they produce a stream of modulated streaks, which are stored in the retina . However the cause of both is the LED PWM intensity control used while braking, introduced by Cadillac around 2000. PWM helps to regulate the full brightness at a range of voltages such on low idle. This can be smoothened by adding a large Cap across the LEDs, but the RC time constant increases as duty cycle is reduced, so it is mroe effective when dim. given brake LED's have an ESR << 1ohm, it would take a rather large cap to filter out 5,000 uSec. Increasing the PWM> 500Hz would make it less noticeable.
"Digital projectors flash images on the screen 144 times per second, for flicker-free motion. But, as with older films, there are only 24 different pictures (frames) per second. Film projectors generally flash each image on the screen 2 times to reduce flicker, using a special shutter. Digital 3-d projectors flash the image for each eye 72 times per second upon the screen." ref