SPOILER!
Ellery is trying to "account for" Ennis. Ennis is obviously a scared man in the closet, so - what is he doing in a gay bar? Married and on the down low, looking for someone to replace the long term lover he lost? If so, Ellery does not want to pursue fantasies about a married man in a dead end situation. Also - he knows Ennis lied about where he is from, therefore, he knows Ennis is covering something up, but not why, and not how much.
So before he jumps in with both feet, he is doing what detectives do - finding out what he really does need to know - is he a criminal? and is he married?