с глазу на глаз
I don't think глазу is genitive here. Is глазу́ locative and stressed on the last syllable, although с usually takes the genitive?
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It actually is the genitive, and the stress is on the first syllable:
The genitive ending -у is retained in quite a few set expressions such as:
Stressed prepositions and particles are also signs of a well-established expression or just a frequently-used collocation:
It is ablative case, a subcase of Genitive. It differs from Genitive in ending and from Partitive and Locative in stress: the stress falls on the preposition if it has a vowel.
и́з лесу, и́з виду, и́з глазу, бе́з толку.
When there is no vowel, the stress fall to the noun: с миру.
The other answer is wrong: the word бро́ду in the examples is actually in Partitive, not Ablative.