If you read Rowbotham's "Earth not a globe!", he seems to think that the vanishing point is somehow defined by the optical resolution: once the distant object gets small enough that the eye can no longer resolve it, that object is at the vanishing point, according to him. Hence smaller objects reach the vanishing point before larger ones. Which is no more than obfuscation or, in plainer terms, bullshit...
Indeed, Rowbotham apparently ties this phenomenon into something to do with the horizon, but exactly how this ties in is vague at best. Thus my call for somebody to give us a specific observation to discuss. Let's choose a specific detail and then see how this applies to it.
First, we can take this claim at face value. Does angular resolution have anything to do with the vanishing point? Well, we must define "vanishing point" first.
https://www.merriam-webster.com/dictionary/vanishing%20point1: a point at which receding parallel lines seem to meet when represented in linear perspective
2: a point at which something disappears or ceases to exist
Normally, I've seen this applied to the idea of a perspective drawing. Parallel lines (railroad tracks) appear to converge linearly into a point in the far distance. We learn that in like 4th grade art class or so. This is just perspective, and it doesn't seem at all related to angular resolution. (At least not yet.) WARNING: A little bit of math can tell you exactly where this vanishing point is, and that calculation does NOT involve angular resolution. Also, that vanishing point happens to land at infinite distance from the viewer.
So Rowbotham was wrong? I'd say no. Let's give him a fair shake here.
As those railroad tracks shrink into the distance, the angular separation between them gets smaller and smaller. At some point, the 2 tracks will be less than 1/60th of a degree apart, and at that point, we can no longer tell where one track ends and the next one begins - they look like a single track. So replace those tracks with a pair of rocks. As the rocks recede into the distance, the 2 rocks will eventually look like 1 rock. Right?
Keep going with this... if we have a rock sitting on a patch of grass, at some point, the rock will fall below your angular resolution, and it will just merge into the grass to become a blurry brownish dot in the field - something that you can't even be sure is even a thing. It will have "vanished."
So based on that, we could argue that there's a "vanishing point" beyond which we can no longer see something, and that is the "vanishing point" Rowbotham is talking about here. Is he wrong about that much? No he's got that right, although I like to point out that a telescope will bring that rock back into view.
But here is where Rowbotham gets super vague. Just because you can't make out the rock against the field of grass, that doesn't create a horizon. Looking out over an infinite field of grass, the horizon is the spot in your view where there is blue sky above and green grass below. A telescope can sharpen that line, but it won't move where that line is.
At this point is where (IMO) the science ends and the hand-waving begins. Once again, I'd like to call for someone to name a specific observation, and we can apply these principles to that observation and evaluate it all objectively.