Eye training usually goes in tandem with weapon knowledge, especially blade work. I’ve learned quite a lot of it in the Wudang lineage of Peter Kim Ho Chu.
Sifu Phil Redmond posted up some cool stuff about eye training awhile back - maybe he could repost it?
In a plain and simple manner, here is how I learned it. Your eyes are your first line of defense, and they are your first line of attack. You look at everything you do. You can see everything that moves in a 180 degrees almost. so you can be aware of any movement that occures from either side, but you must look directly at what your hands are doing. Especially when defending. Your eyes are located on your face in a way to give you depth perception. You have to use both eyes in order to properly gauge your attacks and defenses.
By attacking your opponents eyes, even if you do not actually dig them out of his head, you illiminate his ability to defend against you. I have watched a lot of utube of guys doing Sil Lim, and I am not sure what they are thinking when they similate the eye sweeps. It is done differently I think. Or at least I do it differently.