The means by which you illustrate how a "Be-er" behaves or problem solves may be impacted by the storytelling medium for which you are writing. Screenplays tend to be more visual and therefore require more externalized expressions of problem solving through "being." Novels benefit from being able to describe a character's internal workings without requiring visual action to illustrate internal problem solving.
A Be-er is someone who PREFERS to solve problems internally if given the choice. Some problems require doing, so the be-er may need to do to resolve a problem (like moving an obstruction from his view).
Probably one of my favorite examples of a Be-er is Hamlet. He is charged with avenging his father's death -- a doing problem if ever there was one. How does Hamlet chose to try solving this problem? He changes himself by pretending to be crazy. His overtly odd behavior effects everyone. It eventually drives Ophelia nuts and she kills herself because of it. Unfortunately for Hamlet, his uncle (King Claudius) is too shrewd to fall for the act.
At one point in the story, King Claudius is unarmed and alone while praying in his chapel. Hamlet comes upon him, draws his sword to kill him, but then begins a wonderful example of problem solving through being (and succumbing to his MC Problem of Thought). By thinking too much about his actions, he convinces himself that he shouldn't kill the king right then which is totally consistent with a Be-er's preference for "being" solutions over "doing" solutions. Of course this is only a temporary personal solution for Hamlet and doesn't satisfy the larger doing problem the story has presented to him in the overall story (to avenge King Hamlet's death by kiling Claudius).