When we ask someone "why do you do that?", we are asking for her/his reasons.
This basically looks like to fulfil ones own curiosity. Our intellect is the sphere of our mind and our mind delights in experiencing and knowing. Our past desire or craving to know what creates our current mind faculty.
It someone asks me "why do you play tennis?" and I say "I like to stay fit and I like to have fun. Tennis is good exercise and good fun, therefore I play tennis", I am giving my reasons. (It doesn't matter if having fun actually is a form of suffering. My reasons are still my reasons.)
When you say your reason you are seem to have attachment with your reasoning. Also taking pleasure in playing a game or another hobby or anything else which you call fun.
In light of Buddhist philosophy, would it be right to say that my reasons are the causes of my behavior?
Your behavior is conditioned by pratice not necessarily practice. Also mental constructs which we cling to.
Is there any general agreement across tenet systems? Or is it one answer for Vaibhashika, one for Sautrantika, one for Chittamatra and one for Madhyamika?
I do not understand this part hence will leave it for someone else to fill in for this.
See: Mind, the three words by Piya Tan, 2 paragraphs from the end of page 1 onwards. What is discussed here to attachment to politics, religion etc. but this can be interpreted to attachment to my reasoning, my idea, my view, etc.