I believe establishing e connection has several components:
- Your "look and feel"
- Your energy level and being friendly, smiling and cheerful
- Your ability to listen to the interviewer
- Your ability to ask questions
- Your interests besides career and consulting
1) Look and feel. Try to eliminate the personal root-causes: if there is something more than just case and fit. Maybe it's the way you are dressed, the way you behave, body movement, etc. Do you look mature enough? Do you behave professionally? It may sound obvious, but many candidates miss that. Make a video of your interview and show to your friends or even random people. Ask them if they would personally hire you.
2) Your energy level and being friendly, smiling and cheerful. In many cultures, it is not natural to always smile and you really have to develop that skill. Also, sometimes, when the case is hard, it is really easy to stop get deep into a thought process and get tired. When you get tired your pose and gestures are different and others can easily see that. The only recommendation here is to always control it.
3) Your ability to listen to the interviewer - don't ever interrupt an interview. Listen to him demonstrating your genuine interest
4) Your ability to ask questions. The main objective is to have a good conversation and highlight your intellectual capacity and curiosity.
It is ok to ask:
- Questions that cause positive emotions and highlight consulting pros (e.g. Mck people)
- Questions on the topics you are excited about (e.g. data science)
- Non-business questions (e.g. team retreats)
It's not ok to ask:
- Questions that can cause negative emotions (e.g. work hours)
- Information you should learn before the interview (e.g. typical career path)
- Questions that may show that you are unfamiliar with consulting work (Like are you specialized in strategy or operations?)
5) Your interests besides career and consulting. Talk about your interests. Tell the interviewer what motivates you besides career and money. Don't be too rational. Talk about your friends who work in consulting and their experience that motivates you. Talk about your professors / entrepreneurs / CEOs whom you admire and who were consultants before. Talk about your personal experience of working with consultants. Or about your experience in participating in consulting events. It's always good to have some personal stories that can demonstrate your passion for particular industry or function.