Don’t be shy about letting your interviewers know you want the job. Here’s the way final hiring decisions are often made:
A meeting happens where all the interviewers discuss the candidates. The hiring manager asks the team what they think and who would be the best fit for the group. Some comments are made and if there is not one clear winner, then there is usually some kind of discussion that sounds like this:
“Well, if these two people seem to be about the same level of ability and fit- but this one wants it more then that's who we'll hire.”
The job always goes to the person who wants it more. Be enthusiastic in your interview- not in the thank you note you write afterwards. By the time the note arrives, the decision has been made.
You can prove you want the job through careful preparation, informed questions and body language. Also remember it doesn't hurt to actually say that you want the job! Interviewers want to assume you really want the role or you wouldn't be wasting their time. Make it easy for them, and confirm it out loud.