Vertical and horizontal are the same on FE as well as RE.
What you're asking is, what happens once you reach the far most points of north or south, where do you go from there?
On RE you reverse direction, not changing direct, but once you hit the farthest point north, if you continue in a straight line you end up heading due south and vise versa one you hit the farthest most south point you go north.
On FE this only happens at the north pole, but, supposedly, the south direction (any direction away from the north pole), ends at the ice wall. However before you hit the ice you somehow, magically, turn right or left and spin a circle. I say magically because somehow, with all of our high tech navigational equipment, knowledge of astronomy, , everything remains the same, looks like we're going the same direct.
Yes somehow, after following a southern direct, we turn west or east, apparently without knowing it, go all the way around to the other side of the planet, then turn north and eventually hit the north pole again without realizing we just traveled tens of thousands of miles without knowing it or our equipment detecting it. Some kind of vortex, anomaly, black hole, worm hole, that we can't detect??
What we physically observe is the sun always crossing our path on a journey as aforementioned, but spinning a circle on flat earth you would be following the same path as the sun.
An interesting fact. In a hypothetical scenario if you could leave the north pole on a non stop flight in any direction in a straight line you would end up at the Antarctica, (south pole) on RE, or oe the Antarctic ice wall that encircles FE. The difference is on FE that would be the end of you trip as you could NOT go any farther in a straight line. However, on RE you could continue and eventually end up back at the north pole.