Suppose you're in a conversation with 3 people. Person A, B, and yourself. Currently person A is speaking, directed at person B.
In this case, who is it polite to look at? I know the general rule of thumb is to turn to whoever is speaking, but is there ever a case where one should instead look at the person who the current speech is being directed at, rather than the person currently speaking?
Honestly this is something that has no specific "rule". I believe people just do it unintentionally and after feeling.
When two people currently talk to each other, i mostly look at the person speaking, but for example if person A talks for quite a while i sometimes also look at person B, i believe, to see how he reacts and to see his mimic.
Just look at what currently interests you. If your brain says "I wonder how person B feels about this" look at person B. If your brain thinks "I am very interested/invested in person A's speach" look at person A.
Mostly you will look at the currently speaking person, but simply follow your intuition as this is nothing you can do "wrong" or offend someone.
I would look at the person speaking, or who is about to speak if there is a pause. If I am the one speaking, I look at one person for a few seconds and switch, except I am adressing one of them specifically, then I look at him/her. If I am talking for a long time, I make open gestures, so I am not unintentionally blocking someone with my arms.
I would try not to talk about one person with the other person, e.g "Hey B do you remember when A messed up XY?", because A would feel left out. If you and another person are talking a lot and the third one is quiet, I would try to invite him, e.g "A, what do you think about XY?"
If giving a speach, I draw an eight with my head(slowly!) so everybody feels invited.
EDIT: So I look at the person speaking, because not looking at him is rude (in my opinion) and the other one will not feel left out, as he can look at the person speaking aswell. If you speak and no one looks at you, you will feel left out and awkward immediately. If I am the one speaking, switching from one to another is a simple technique, so everybody gets attention, if I adress someone specifically, I look at him, because that undermines my intention to adress him. Supporting your look with your gestures is an easy way, of inviting everyone into the conversation. Imagine your arms draw two lines, and everyone between those lines is part of the conversation.
I am not talking about one person with another one, because he will feel left out very easily, this is based on personal experience (sorry). Inviting someone by adressing him, is my way of giving quiet people a chance to join the conversation, obviously if they do not want to join, do not do it :)
Drawing an eight is just one way to ensure, to look at the whole crowd. It does not matter if there are two or two hundred. If you draw an eight, you look at the center and each corner and your head moves smoothly. Same thought process when talking to two people and looking at everyone for a few seconds.
As a very generic rule of thumb, it's common to start with looking at who's talking.
Please notice I said "start with".
Later on during the speech, it all depends of what is being spoken about.
If the speaker is speaking about himself or someone/something currently not present, you may want to keep on looking at the speaker with occasional glances to the third person if you feel like.
BUT
If the speaker is speaking about the third person, you may want to mainly look at the third person e.g. to perceive reactions. This is the classical case of job interview: one is you, one is talking to you and other people are looking at you in order to analyze how you behave.
So, in the end, it strictly depends on the context.
