Pursing of the Lips is a nonverbal that is made by someone who, at least in that moment, perceives himself and his position to be an alpha (relative to the antagonist at hand). It also is a signal that they believe their plan/opinion/answer is superior - however they will only be sharing a part (perhaps none) of it openly. Because they are the relative alpha - they also believe they have a reasonable chance, the resources and power to successfully execute their plan.
Think of the lip purse as a signal of clandestine disagreement and strengthen your "Plan B" for an ambush.
You may not have a master tactician like Senator Reid across the table from you - but you should never take a lip purse casually.
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