Like whether the singer made any attempt at all to involve the audience

Depends what you mean. The first time I sang at a folk club I looked straight ahead, caught somebody's eye, thought "Christ! People are looking at me!", flinched and looked up. Then I found I was looking straight at the window in the back wall, with a streetlight beyond; that suited me, so I sang to the back wall, which was about 40 feet away (it was a long room). I think it worked OK.

These days, on the other hand, I find I'm singing with my eyes shut more and more - not catching anyone's eye means that I can concentrate on the song. Again, it seems to work - and certainly there are some singers who I find very engaging, despite them singing with their eyes closed.