It would work the same way on a flat surface, too. Almost everything would work the same way, it largely comes down to interpretation of observations that differs, where I think the views don't align.

There is an effect called coffee cup caustics which quite adequately would explain the sun within the model. On the physics front, the models are very much equivalent, but when it comes to theoretical models of how it all works and looks, that tends to be speculation because only so much can be verified in person. Private citizens cannot explore the outer regions, only guided tours are allowed and it could cost 6 figures or more, plus the ol gov reserves the right to take your money and deny your application.

The disc thing is intentionally put out there to mislead people and make it seem absurd. We definitely observe round bodies in the sky, it can be argued whether or not they are spherical, but that wouldn't necessarily mean the Earth is too. This is a pretty good video that combines the unifying expression and shows a lot of how the model could work, and these geometric patterns work exactly the same way that magnetic fields do, within the non-mainstream explanation of magnetism. The plane (Earth) is the same as the plane of inertia in a magnetic field. It is known that the earth has a downward bias with a negative charge, and there is an measurable equipotential (steady) increase in electric charge the further we get off the ground. It is why lightning discharges on the Earth, always taking the shortest route and expressed in the same pattern. We can manipulate electrostatics in a way that can explain the phenomenon of gravity in a much more plausible and understandable way than through relativity, which is based on mathematical equations rather than repeatable experiments.

While I agree there are compelling arguments on the globe side, I consider the evidence stronger on the other side when it is properly examined, at the very least, a lot of it falsifies the globe model as it is taught. I'm open to it all being a simulation of sorts too. The oddities such as intentionally edited videos of the alleged 24 hour sun from Antarctica should arouse suspicion in any skeptic, because if it was true, there would be no reason to edit and lie about the footage. A 24 hour sun in Antarctica would be a big problem for FE.

Ultimately I try not to force my view, but I encourage curious people to give the topic an honest look, because it could change your entire outlook on everything as it did for me and many others.