I think "the left eye" in this particular case (a photo of a skull made of pancake batter) is still very slightly ambiguous. "The skull's left eye" would not be.

Interesting, because I would say the opposite. "On the left" suggests left of image, "the left eye" could be any version of left.

I guess there's some ambiguity regarding whether or not this can be ambiguous. Because it seems like it can to me.