Let's start with the first image, the ancient Egyptian Eye of Horus.
The Eye of Horus was an amulet of healing and resurrection. One of the most revered and powerful amulets in ancient Egypt, the Eye provided protection from evil. It was a symbol of royal strength and assisted in the rebirth of the deceased.
As the granddaddy of apotropaic amulets, meaning a talisman that turns back harm or evil, the eye amulet was so popular that it spread throughout the region and the centuries, morphing and adapting to various cultures, but always retaining the staring single eye. It is truly very old magic.
The Eye still exists in various incarnations even today. It is very popular throughout the Middle East, especially in Turkey where it is known as nazar boncugu. In Turkey you will still see this amulet nailed over doors to homes, decorating the hulls of ships, and pinned to the clothing of young children, placed there protectively by their loving mothers. (Actually, you see it EVERYWHERE! :-)
Now let's look at Mad-Eye's mad eye.
From Goblet of Fire:
But it was the man's eyes that made him frightening.
One of them was small, dark, and beady. The other was large, round as a coin, and a vivid, electric blue. The blue eye was moving ceaselessly, without blinking, and was rolling up, down, and from side to side, quite independently of the normal eye -- and then it rolled right over, pointing into the back of the man's head, so that all they could see was whiteness. (p. 184-185)
Hmm. An all-seeing round eye with the colors of black, blue, and white... Ya think there's a connection?
A few years ago, when E.L. Fossa of Wizarding World Press pointed out to me the similarities between JKR's creation and the Turkish nazar boncugu, I felt a bit dimwitted. Here I was, married to a Turk, having lived in Turkey many years, with many boncuks hanging in my house, on my keychain, or pinned to my children's clothes when they were babies, and I'd not made that connection. Yet, I was only then learning how to look below the surface in a Harry Potter novel.
If I'd had any remaining doubts that JKR intended for the reader to make these connections, it was was when she had Umbridge nail Mad-Eye's glass eye to her office door that cinched it for me. On the surface, that was just a bit odd. And you can bet, whenever JKR is doing something that seems odd or slightly out of place, that she's getting at a deeper meaning, most likely using a mythological reference.
But ... why would JKR pin a benevolent amulet onto a character who in the first book is a Death Eater and fraud? I think there's an initial reason, and then a deeper one that leads to the underlying mystery of the series.
First the initial reason -- the Eye of Horus, as well as its descendant, the nazar boncugu, are amulets that represent protection from an all-seeing divinity. In Goblet of Fire, pseudo Mad-Eye (aka Barty Crouch, Jr.) fills this role. He sees all, knows much more than any other character what is truly going on, and is bent on protecting Harry and getting him through as champion in the Tri-Wizard Tournament. Unfortunately, all this protection is aimed at providing Harry as a sacrifice to his lord and master, Voldemort.
However, in the end, despite himself, Crouch's protection works effectively. It is Barty Crouch as Mad-Eye who taught Harry how to throw off the Imperius curse, an ability that helps Harry survive his encounter with the Dark Lord and return safely to Hogwarts.
As writers, we have the option of working sub-textual meaning into our stories. If we do so with skill and resonance, as JKR has done with Moody's eye, then we've provided a whole new layer for the reader to engage within our pages, time and time again.
So, why would JKR draw so much attention to this ancient Eygptian amulet? I have a theory and it points to the Horcruxes. But that's a huge 'nother post. I'll try to do it this weekend, so check back.
Eye of Horus
Door with Boncuk, Turkey