> But my sense of it is that it is a neurological phenomenon, the brain and the eye working together ...
Yes, that's correct -- it's both.
> So I still conclude that light falls continunously on the retina, and is continuously processed.
Yes, unless it's periodically interrupted, as with a flashing source. In that case, it's a discontinuous flow of visual information that we must assemble into something meaningful.
> to make sense of a visual phenomenon that does not exist in nature, but only under artificial circumstances.
People are wired by natural selection to fuse a discontinuous series of images into an apparent continuous sequence on the ground that this makes us more fit to survive -- so it does exist in nature, it's not artificial.
Consider a primitive man, or one of humanity's predecessors in the long history of evolution, watching a prey animal running through a forest. Our distant relative sees the prey animal between two closely spaced trees at one moment, then sees him between two other trees a bit later. With this limited information, he is able to infer (a) the prey's speed, and (b) where he will be five seconds from now, where he intends to be. This is all based on our ability to ... wait for it ... fuse many discontinuous images together.