In business and in life, copying someone's behaviour can build a rapport. In an interview setting, that might work against you if the interviewer is annoyed.
Photo by the half-blood prince
The Journal of Experimental Social Psychology explains how an interviewer's mood can change the mood of the applicant:
interviewer tone had a significant indirect effect on applicant performance through its influence on applicant tone. Nonconscious behavioural mimicry of negative behaviours occurs in social interactions, is not always associated with positive outcomes
This study was small — only 54 participants — but it's a useful principle you might easily forget in the heat of the moment. The key is to be conscious that the interviewer may be changing your tone or behaviour. If they aren't "into" the interview, don't let that change your attitude. Stay upbeat and positive even if the person on the other side of the table has a case of the Mondays.
The tongue-tied chameleon: The role of nonconscious mimicry in the behavioural confirmation process [Journal of Experimental Social Psychology via Science of us]