You answered your own question - she does it for people to impress upon her their own emotions. That way it seems she has emotions, because in fact she has no emotions - she feels nothing, except sometimes rage, or a smoldering hatred. That's it, but she can't portray that publicly. So she opens her mouth and stares and smiles and you never guess she's doing that because she's totally insane - and you fill in the blanks yourself, according to your own sensibility.
Most of what she does is like that. The closer her associates, the closer they imitate what she really is - dead hateful. Everything else is just lies. Her biggest secret is that she isn't even human. She's not alien, though - her soul is just dead. She's more a bot than anything else.
Bill does the same mouth-open thing. It does look deranged. Their “smiles” never reach their eyes.
Thanks and well stated.
I agree, especially after opening my mouth wide - like for the dentist - and trying to come up with an emotion that would justify that action - nothing comes to mind - it feels a little insane.