I want to use a idiom or phrase that describe the emotion or gesture

I think you are talking about describing both a gesture and a state of mind. I don't know that there's a single word or phrase for what you described. However, you can describe what the character is thinking, feeling or doing. You can do all three, or focus on one aspect. Here are some ideas that might be helpful:

She paused, contemplating the situation.

She appeared deep in thought, a finger pressed to her lips.

He looked hard at the painting, his finger touching his lips, forehead creased.

Michael adopted a "thinker's" face -- index finger at his lips, eyes looking far away.

Their father seemed to be calculating, with eyes half-closed, his left index finger slowly tapping his lips.