I'm always getting covered mouth and hidden eyes mixed up because 'hidden' and 'covered' practically share the same concept. Should there a cleanup so both of them use 'covered' or 'hidden'? Are there also other tags for these that I'm not aware of?

Hidden eyes appears to be used synonymously with hair over eyes which is a much better established tag. Unless we need the additional generality, I'd move we alias in that direction. If we do need it, we should have an implication in the direction of whatever we decide the more general tag should be named.

Covered is probably better than hidden. I'd use it in a wider variety of ways. or covering_mouth / covering_eyes really. I wouldn't alias to hair_over_eyes though, because I'm sure there are many images of someone putting their hands or something else over someone's eyes.

In that case we should add hair_over_eyes → covering_eyes as an implication.

Covering_eyes (<-- gerund) is the action of using your limbs (arms, hands, anything prehensile) to actively cover your or someone else's eyes.

Hair_over_eyes happens naturally and is an artistic style.

What about blindfold? I think it belongs to that tag group as well.