Which word refers to the careful and disciplined observation of a person?

The term that accurately conveys the idea of careful and disciplined observation of a person is "surveillance." Surveillance involves monitoring individuals or groups, often for security, legal, or investigative purposes, and is characterized by its systematic and focused approach. This term is frequently used in contexts such as law enforcement, security operations, and research where attention to detail and ongoing observation are crucial.

The other terms, while they have their own meanings, do not fit this specific definition. For instance, "vacillate" refers to the act of wavering or being indecisive between options, which does not relate to observation. "Vilify" means to speak or write about someone in an abusive or disparaging manner, which implies negative commentary rather than observation. "Verbiage" pertains to an excessive number of words or language that may be unnecessarily complicated, which is unrelated to the concept of observation. Thus, "surveillance" stands out as the most appropriate choice for describing disciplined observation.