there shouldn't be any intersection between the Suns disc and the horizon at all, just a fade to zero at the horizon.
Why would there be no intersection?
Any object that moves away into the distance until it can no longer be seen will intersect at the horizon vanishing point.
It will disappear from the bottom up at vanishing point.
The Dave Weiss kitchen counter top video demonstrated the intersection at the horizon vanishing point with the sun disappearing from the bottom up.
The quarter across the table experiment shows the intersection at vanishing point as the bottom half slowly disappears more and more.
The hallway photo I shared demonstrates the intersection at vanishing point.
The vimeo video Lad posted earlier in this thread demonstrated again and again in real life and with diagrams the intersection at vanishing point at the horizon.
Artists have to study and understand how the intersection at vanishing point works.
Mountains will disappear from the bottom up the farther away you go. The closer you get the taller they get and the more of the bottom half you can see.
If you photograph a mountain at 50 miles away and then at 100 miles away and then at 150 miles away
the mountain will appear to be shorter and shorter each time.
The bottom half will disappear more and more
the top half will remain visible until you go so far away even that is no longer visible.
Look at this drawing:

Art teacher says to redraw this photo as if you have traveled 20 miles closer to the mountain.
What would you change about the mountain?
You would show more of the bottom half.