Is the final answer for understanding behavior in physical terms BRAIN ACTIVITY? Perhaps, eventually, this will indeed be part of a good understanding.
BUT, brain activity DOES NOT (as seen) point clearly, i.e. POINT AT ALL WELL, TOWARDS IMPORTANT BEHAVIORAL PATTERNING (the MOST important) -- that which we want to understand and really need to understand. Yet over and over, people cite neuroscience as not only associated with understanding "behavior", but as the WAY to do so -- and to get to the ultimate physical terms. It is not. In fact, it is MUCH, MUCH more arguable that we must discover the patterning OF the most important sorts of responses we have before we can have any decent clue about what these behavior patternS must have correspondences with in terms of brain activity (what related "brain activities" "look like").
Behavior is parallel in ways (many, and very likely different with development) AND the several various faculties which operate (even when sequential) need to be SORTED OUT IN DIRECT OBSERVATIONAL STUDIES OF BEHAVIOR PATTERNS -- not only are they fast, but they are SYSTEMATICALLY VARIABLE. It should be clear that anything significant seen in brain activity related to major (but real, and species-typical or species-specific) behavior patterns IS PRESENTLY necessarily confounded, and the "answer" cannot come from brain science itself -- for that is the very confounded activity I just noted. To argue against this is to essentially argue against any like an experimental-type of investigation, where just one or a few variables are what is being explored.
So, in fact: The real, ultimate, physical understanding IS IN TERMS OF DIRECTLY OBSERVABLE --> OVERT