I'm not exactly a singer, but rather I would say I am replying from a audience point of view.
I think many times, we have seen cover bands at bars and gigs doing what they are best at. To perform, to influence and bring love and emotions through music. But the feel of a song is utterly far from present.
Eye contact with the audience is important. It's a form of "sincerity" onstage, which can somehow contribute to your stage presence.
And also may I suggest, that you yourself feel the vibes of the song as you sing? Why? The reason for being so, we have seen tonnes and tonnes of bands' vocalist sing like reciting dictations in school. We really don't need someone to show the audience that he/she can memorize the lyrics well. Anyone can memorize lyrics and chunk it all out on stage.
It all boils down to delivery... I see that as a very important aspect for bands and particularly the lead vocalist. (Just try and imagine how some Jazz singers capture the attention of their audience.) Sing like as if the song belongs to you...
DD