They do apply in all directions equally. If you are in a forest looking up at tall redwood trees you can also see that they seem slightly tilted at each other. The earth is a plane which stretches outwards from you until the lands reach the vanishing point. There are more things on the earth than high in the sky, so the effect is more visible.
If there are converging perspective lines in all directions, presumably they also have vanishing points. So why in your model is the sun visible when at it's highest in the sky mid day, but not after sunset? Are you saying that the sun is closer than the vanishing point at noon but past it after sunset?
If the trees in the above forest-perspective example extended hundreds of miles into the air, perhaps the trees would intersect and block out the sun.
Why are trees relevant to answering this question? I'm quite sure a tree can block the sun given proper combinations of height and angle. It's called shade.
Are you saying that vanishing points exist because things block the view?
Yes.
What things are causing the vanishing point (and blocking the sun) when I see a sunset over the ocean?
Any tiny waves or swells that breach the flat surface.
The perspective lines may be perfect, but the surface of the earth is not perfect. In Earth Not a Globe the author points out that the sunset happens sooner than expected if the conditions of the oceans are more disturbed.
Just to be sure that I'm understanding what you are saying.
Example scenario. I am standing on the coast of California, looking west, watching the sun set. Just using rough approximations for the sake of discussion only. If the sun is at its highest point at noon, it would be at the opposite side 12 hours later, so that would mean it would about 1/4 of the way around at sunset, let's say 6 pm. Based on your unipolar map that would be around eastern Australia.
You are saying the sun is at so low of an angle above the Earth, that tiny waves and swells are what block us from seeing the sun after it sets from out perspective.
Is that correct?