I'm looking for parallel idioms related by vocabulary and/or meaning.
Γλαυκῶπις, -ιδος (L. glaucōpis, -idis)
This has already been mentioned in the Mythology question you linked, but I think it's the best idiom for your usage.
This is a Greek word, but one famous enough that educated Romans would recognize it (especially as glaucus is attested in Latin). It's a compound; the second part is pretty clearly ὤψ/ōps, "eye" (as in optics, optometry). But the first part, glauc-, is more interesting.
Γλαυκός/glaucus is a curious word with no known cognates. Its earliest meaning, as found in Homer, is probably "shining" or "gleaming", with no reference to color. Later it shifted to mean "silver" or "gray", and then to something bluer, what we would now call a "steely" color (it was applied to olive leaves and certain other plants, as well as the ocean).
From the meaning of "shining" came the noun γλαῦξ, γλαῦκος/glaux, glaucis, "little owl", because of how their eyes shine at night. Because the owl was a symbol of Athena, γλαῦξ was often used in reference to her: we find idioms like γλαῦκ᾽ Ἀθήναζε "owls to Athens", the equivalent of English "carry coals to Newcastle".
So γλαυκῶπις could mean "with shining eyes", "with steely eyes", or "owl-eyed". When used as an epithet of Athena, all three are fitting.