how does your spotlight make a pool of light the shape of the yellow area in the gif below?
((red dot indicates position on earth's surface where sun is directly overhead))
You don't get night on a flat earth without resorting to obvious lies about the nature of geometry, perspective and optical beam paths unless you resort to 'spotlight' description.
No spherical light emitting object over a planar disc surface makes an illumination pattern like this either.
However understanding that the azimuthal projection map is a device for rendering a globe on a 2d surface, and looking at a 3d model of sunlight on a globe varying over seasons with respect to axial tilt, observational reality matches perfectly with model.
Too bad, but flat earth models simply do not represent reality.
Anyone reading this still think earth is a flat disc? Then do something useful. Quit repeating thoroughly discredited, false statements and lying models, and come up with an actual model that actually reflects known physical laws and actually is able to describe well known, observable, repeatable, measurable phenomenon like sunset, lunar phases, daylight distribution, the movement of stars in both hemispheres, etc etc etc.
Everything else you say about this is waste of time. All your arguments have already been repeatedly shown to be flawed and wrong. If it's reality, you should be able to describe it in a way that actually works. No such model exists that I've seen in over 20 years of discussing the topic. So you believe the earth is flat? Then go find that true model that stands up to inspection and criticism. All those arguments you have now? Not one stands up to scrutiny.