In his commentary to Bereishis 2:7, Rabbeinu Bachya cites both views regarding whether the soul is indivisible or tripartite. He notes that according to the latter view (which is that which Ramban says is supported by Chazal and which Ramban favors), whereas the vegetative soul is spread throughout the body, the rational soul is housed in the brain:
הנפש החכמה נמצאת באדם לבדו בה משתתף עם העליונים הקדושים העומדים לעד לעולם בחכמה ושכל ומשכנה במוח והיא הנקראת נשמה שנאמר ויפח באפיו נשמת חיים
Rabbeinu Bachya continues to note that while the account of the golem in Chazal supports the view that man contains three souls (of which the golem only possessed two), Scripture indicates that the soul is indivisible. Nevertheless, he does not appear to clearly decide the matter, and the point that is concerning him, and which he stresses, is that both views agree that the soul lives on in the next world after death.
Interestingly, whereas Rabbeinu Bachya here makes the unqualified statement that sechel is housed in the brain, in his commentary to Bereishis 1:26 he says that sechel comes from the brain and machshavah comes from the heart, and in his commentary to Bereishis 6:6 he says that the heart is the kli for machshavah, which originates in the brain. It seems that Rabbeinu Bachya was seeking to accommodate the Galenic view, of the mind being housed in the brain, with the traditional view found in Chazal that the heart houses the mind.
What can we take from Rabbeinu Bachya's writings for the modern dilemma of whether brain-death is death? Well, although he himself does not take a definitive stance on the nature of the soul, it does seem that he believes that if the soul could be differentiated, then the human part of it would be housed in the brain. The brain is the seat of the mind (even though he was also hanging on to the ancient view that the heart is also involved), the mind is what defines us as human beings, and thus the neshamah would be in the brain and manifest itself through the brain's activity.