"Gay face" is a term I wish good people like Carlos wouldn't use.
It's a term like "fag hag" that ultimately dehumanizes both the person being described and the person using it. Such phrases really only work in a rarefied, ghettoized setting on two or three cocktails at closing time when the atmosphere is thick with bitterness and self-loathing and no one is listening but the like-minded.
Outside of that cozy, smug and self-satisfied atmosphere, these phrases are nothing but slurs.