Echopraxia

Echopraxia (also known as echokinesis) is a disorder characterized by the involuntary copying or imitation of another individual's actions or behavior. A person suffering from this condition will compulsively imitate the movements or behaviors of a person around them. Echopraxia is sometimes a symptom of autism spectrum disorders, schizophrenia, catatonia, and Tourette’s syndrome.

For example, when observing a person near them touch their nose a person with echopraxia may involuntarily begin to touch their nose.