The nature of the dragon eyes is yet a mistery. Of course, together they were able to become nidhogg's shadow (niddy himself dead by Estinien hands, and we banished his shadow, so no more niddy as individual consciousness with a purpose is left). Separated they were powerful enough to fuel a god-banishing-from-existence sword...

I think the eyes are first, nearly indestructible, only be able to be either consumed (as the first heavensward did) or you get possessed by them, the first heavensward went a long shot thanks to consuming the eyes, fighting a fully powered niddy and taking one of his eyes out, and even that wasn't enough as thordan died in that encounter, haldrath the first loldrg finished it off, and then they decided to not consume them (something we never got explained, we know they ultimately sealed Haldrath away cause he also got consumed by the eyes).

So is either a thing of consuming the eyes first, before they consume you, there is maybe a diference between Ratatoskr and Niddy, since she, for all we know, was much more peaceful, she might have been weaker, her escense more easily tamed and that alone was enough to allow the first heavensward to consume her eyes, yet they were not strong enough to do the same with Niddy's, his personality and escense had to be first purified from the eyes, thing we did, just like you prepare food for their consumption, we prepared those eyes, purified them and now they are ready to fuel a new master.

I also think, the eyes are nearly, if not completely, indistructible... They only logical reason to do with them at that time being was to quickly cast them away somewhere no one will ever reach them (Azhys Lla was the location picked by the first heavensward and we saw how that went...) The abyss underneath Ishgard wasn't honestly a bad choice, once again, we were attacked by an Ascian Ex Machina.

Either way, it makes a lot of sense, at least for my and my crazy theories, that the eyes are back.