It isn't just day and night.
It is how day and night are distributed over Earth.
If Earth was flat, the entire Earth should have day at the same time and night at the same time.
Even if you wanted to appeal to a spotlight just illuminating part of Earth, you would need a magical shape shifting spotlight that illuminates a very strange and non-circular region, and the direction to the sun still wouldn't match.
But a much better proof is the position of the sun and other celestial objects around Earth.
A great part is the existence of 2 celestial poles, always 180 degrees apart.
They can be observed through timelapses of the stars, with all the stars appearing to trace out circles around them.
You can also circumnavigate these poles, i.e. keeping them to one side, you can follow a path along and end up back where you started. This means that the point on Earth below the pole (the sub-polar point) is a finite distance away.
For a FE, this makes no sense:
If you pick 2 locations (preferably on the equator so both poles are visible at once), you can draw 2 straight lines. These lines go towards both poles (or perhaps more appropriately, the sub-polar point.
Because both of these lines go to both poles, this means you have 2 straight lines, intersecting twice after some finite distance. This is impossible (ignoring the complexity of a flat torus).
In order for 2 lines to intersect twice, they need to be curved.
This makes perfect sense on a RE, as these lines are curved, following the curvature of Earth.
The sun never stands vertically on earth.
No, it always does.
You can observe this yourself if you are within the tropics.
The sub solar point remains within the tropics, drifting north and south over the year.
If you go there and wait for the right time of year, you will observe the sun directly overhead.