I will not begin to explain to you all the differences between Eternal and Mortal. But for our subject, in your map, Eternal eye will probably mean any creature that can see through normal invisibility (like the Doomguards or the Undead Shade). So when you creating this ability all you have to do is to make it unseen to all the creatures with the ability to see through normal invisibility (it will be very cool to create such ability, name it "Eternal eyes" and to just give it to anyone who is worthy, to your opinion, to be an Eternal.)
Level 3 of the ability is meant to make the banshee invulnerable to anything that can cancel the effect. Imagine your self if the enemy is using powerful magic that causing damage to everyone within its area, and you don't want your banshee to get hurt. So this is the way to make your banshee completely undetectable. Level 3 will also allow to your banshee to become unseen against guard towers (or any other structure) with the power to see invisible units.
Edit: If you want you can add to level 1, level 2 and level 3 the ability to see invisible units.