Writers often wonder how they can build mystery into a character. I know I used to. I used to wonder how to portray lots of things. The best way to learn how to portray something is to think about what it is that you want to portray and then break it down into it's elements and then portray those elements.
So, if we want to portray a character as mysterious we need to think about what the key elements of mystery are. Well, one of them is the fact a mystery is a question that we just can't find an answer for. There are suggestions as to the answer and multiple people might have different interpretations as to the answer which, of course, just adds to the mystery even more.
Well, one of the best ways to pose a question that has no answer is to use a muted theme. For example, if a character does something odd once and once only it poses a question but will be forgotten soon after. However, if a character does something odd on an on going basis there must be a reason for this odd behavior. What could it be? We are intrigued and want to know why they are doing this. It must serve some purpose.
I believe I first learned about this technique in an academic study of The Bible entitled The Book of God. If I remember correctly, in this book the author investigates the odd habit Sampson has of cutting the ears off of prey he has killed. What significance does this have? Why does he do it? What does it mean? It must have some greater significance because it is in The Bible. Nope. The author concludes that it is simply the use of a muted theme to increase the mystery of the Sampson character. We will never know why he does it and that is the point...and the desired effect on the reader.