A couple quick tips I found from two of the founders of Animation Mentor.
Animating two characters (Reference: CGChar)
"I think my biggest tips would be:
1) film reference with a friend(s). Don't try to do reference of 2 characters acting with each other by yourself by filming one and then the other. You'll miss out on many opportunites to subtly interact that you would discover by filming reference with another person physically in the scene with you. Even if the characters never actually touch, this is a really important step.
2) Be very careful about leading the eye of the audience. It's better to have one character bordering on "dead" than having the audience not knowing where to look. Most importantly, make sure it's very clear which character is talking when. Overacting can wreck a scene, but it can doubly wreck a multiple character scene because you can't tell who is talking or who the animator wants you to be looking at.... Anticipation can help you direct the eye of the audience, as can staging/composition, etc.
Anticipation is one of the big ways though. It's like your secret line of communication with the audience. "hey - look over here because something funny is about to happen!" or maybe subtly moving a character's left hand just before he waves with his right gets the audience to switch over to look at that character and not miss the wave... "
Leading with the eyes of head (Reference: CGChar)
"I usually think of this this way. Of course, like everyone pointed out, there are no rules...so don't animate a certain way just because someone said so.
I think about eyes in different ways, but the main drive to animating the eyes is where the interest/force comes from. Not so sure if that makes much sense. If you are talking to someone, and a third person calls you, the eyes can behave different ways:
1) If you are really really interested in this third person that's calling you (maybe the girl of your dreams, who knows...), then for sure I'll have that character lead with the eyes.
2) If you are really really interested in the conversation/subject you are having (more than who is the third person calling)...then I'll start twisting the body, then the chest, then the head, and I'll have the eyes be the last thing that turns. Mostly because his head is still in that conversation with the guy.
3)If the third person pushes you from behind, same case as number 2. I may have the eyes move the last (after the head).
It's all a matter of exploring. But I agree with Shawn, for the most part, I'll lead with the eyes...but always thinking about the force driving the action."