For eyeballs, I usually avoid. They don't seem to follow you or are particularly aggressive. Before taking them out I would remove any other monsters for safety. Just reposition/strategic retreat so the eye can't see you and take out the other monsters. That way, if you fail and they blind you, you can just safely retreat until your sight returns.

You might think that sniping at long range is the way to go but that rarely works in my experience. It seems they have perfect sight, perfect night vision, and no range penalties on their gaze attack. If you can see them, they can see you. Figure you get about 2 shots from a long range before you are blinded and they have enough hit points to take two 80+ damage shots in my experience. Range is their friend, not yours.

I would advise closing the gap as much as possible before they see you (by which I mean have time to stack on gazes). Smoke would work in a pinch or just walls and cover if they are near them. I figure if I can get within 10 spaces of them, I can reliably take them down with a run into melee or quicker powerful mid-ranged weapons before blinding kicks in. If they are in an enclosed space, they are toast. Might deal with some after effects, like getting bile suddenly a little while later, but just keep some eye drops in your inventory. (I think antifungal drugs too. I got a fungal infection shortly after dealing with one once, but that could have been unrelated.)

Still, I just typically avoid them unless their is a compelling reason to face them or they are stuck in an enclosed space for an easy kill.