If the earth is flat the Sun should always shine on us. It would light the whole Earth equally.
You are applying a round earth concept to a flat earth theory. Can't do that. In FET, the sun acts as a spotlight, directing light to a limited, circular, area. FET assumes the sun is also NOT a sphere.
I have recently experienced a phenomenon that, to me, is proof the earth is ROUND. I would have a hard time convincing anyone of this phenomenon though.... here it is:
I returned from a vacation to Colorado a few days ago.... as I was driving cross-country through the VERY flat state of Nebraska, I observed the lovely, endless, corn fields that stretch for miles and miles in all directions. It just so happens that this time of year the corn is right about eye level when driving on the interstate in my van. As I looked across one field, I could see the flat surface of the tops of the corn as though it was an ocean of corn. If you understand calculus and statistics, you can understand that the average height of all the corn in that very flat field was the same for each corn plant - there is not any significant deviation from the average height. This allows you to observe the corn field as a flat surface, or an ocean. In looking across a corn field (at nearly eye-level), I could see the tops of the corn for about 1 mile or so until strangely enough, the tops of the corn disappeared. In other words, there appeared to be a 'hill' and the tops of the distant corn faded below the nearer corn. That seems consistent with the mathematical conclusion that if the earth is round, it should dip about 8 inches per mile. The distance that I observed this effect was too short to attribute to the perceptual effect. The difficulty in proving this, is that someone can easily say, "How do you know there isn't actually a hill in the corn field?" Well, I can't without surveying the entire area. However, being from Nebraska, I know that these flat spreads of land are REALLY flat, and have no hills. I observed this in multiple corn fields during my 6 hour drive through Nebraska. That is my 2 cents.