Yes, I think that the light being stationary is an important distinction, though it's a good thing to control for because motion complicates things.

I came to the comments here because of a flickering effect (different from what they're testing for) I often observe: the tail lights of cars. Sometimes when I move my eyes (not my head) very quickly I will see a dashed trail from the red tail lights of certain cars (I'm assuming they're pulse modulating for some reason). I've been thinking about this in terms of the often-cited phenomena where our brains 'black out' our vision briefly when moving our eyes. I think this (brain 'blacking out' our vision) is not what happens, and some others have similar evidence: https://www.science.org/doi/10.1126/sciadv.abf2218