On the oracle bones, 高 is a watchtower seen from outside: a peaked roof over a tall shaft, a small window partway down, and a solid base with a doorway standing high above the ground. Anything that towered — a building, a wall, a person — borrowed this drawing, and 高 has meant "tall" and "high" ever since.
A piece of culture
Beacon towers on the Great Wall Centuries after 高 was first carved, soldiers along the Great Wall built tall beacon towers (烽火台, fēnghuǒtái) that still echo the watchtower drawing at its root. By day they signaled with smoke, by night with fire, and a chain of these towers could relay a warning about approaching enemies across hundreds of kilometers in a single afternoon — long before any rider could cover that distance. You already know 火 (fire) from Chapter 1: the same signal fire that lit those later towers.