TL;DR: Our senses are not sufficient by themselves to determine the shape of the earth.
As we already established earlier, there's no other mechanism with which you can perceive the earth. Everything at some point must filter through your senses, therefore your senses alone are the only thing you can use to determine the earth's shape.
Fine, and I don't disagree with that. Of course ultimately our senses are how we perceive anything. But that's not the same as saying that we can build evidence for a flat earth just by looking at stuff. This quote from the Wiki, from the FAQ:
The evidence for a flat earth is derived from many different facets of science and philosophy. The simplest is by relying on ones own senses to discern the true nature of the world around us. The world looks flat, the bottoms of clouds are flat, the movement of the sun; these are all examples of your senses telling you that we do not live on a spherical heliocentric world.
Is stating that us just looking at stuff is evidence. And sometimes it is, but let's take those examples one by one:
The world looks flat - that isn't evidence either for or against a flat earth.
The bottoms of clouds are flat - not even sure that one is true, even if it is I don't know what bearing that would have on the shape of the earth.
The movement of the sun - this one is ironic given that a core FE belief is UA which is used as a substitute for gravity, the claim being that it would be indistinguishable from gravity (true in many ways but the Cavendish experiment is demonstration of gravity as a force). Point being the exact same thing applies here. The sun moving across the sky would look exactly the same if the sun went round a stationary earth or the earth rotates and the sun remains still (relatively, let's not go down that rabbit hole).
None of these things are evidence for or against a flat earth. And the horizon always at eye level page is basically one long "well, it looks like it's at eye level, so it is". Case closed! No controlled experiments are outlined on that page. Yes, if we do a controlled experiment we are using our senses to look at the results but that's not the same as just looking at the horizon, figuring it looks pretty much at eye level and saying that is evidence for it being AT eye level regardless of altitude.
There seems to be an emphasis of what you can perceive rather than what you can measure.