Yeah, my understanding is that the side depends on context but also eye movement, like with the "check that out" you can move/roll your eyes to the side you're pointing to to signal that, while the "come over here" is a quick move to the side you're pointing and moving back to the center

You can also count mouth movement too but that depends on the person, some faces are rock solid and don't move unless they talk and some are doing all kinds of facial expressions