Haven't you heard of the new "personal sky" theory or the donut field theory?
Honestly, that thing where they map sun position, is nothing more than putting the data on the flat earth map, and OOHing that it makes a cute picture. Not one that makes any real sense necessarily, it just looks kinda cool. Meanwhile putting that data on a globe just points to the sun. BOOORING! Like the flat earth picture better! Want flat earth picture!
The personal sky theory is quite nebulous but usually involves refraction. In that sense, flat earthers assign a VERY important job to refraction: GET THE SUN WHERE ITS SUPPOSED TO BE DARNIT! This is a job that needs high precision and stability (in order to match orderly reality), and refraction is not known for always behaving precisely and stably. In addition, they need stunningly powerful refractions, bending in the opposite way to what we expect. (we have good reason to believe refraction bends toward higher density, not vice-versa as flat earthers need) I view this theory as another absurdity.
SORRY, tangent: to bring this back on topic: no, perspective does not set the sun nor get it in the right place. They need other mechanisms such as refraction etc.