I have a hard time thinking of any behavior as completely unaccountable for by the brain. What is hardest to account for depends on how we define terms. The more abstract something is that we denote as behavior, the more difficult it is to account for. Also, no behavior can be seen as all or none as perhaps the presence or absence of an object on a table. Even that is debatable if we reduce the object to subparticles, in which case the object may only be partially there.
At some level, everything involves the brain. That is, the brain is accountable for behavior in the sense that it receives input through our senses: input which may or may not result in an observable response. "Observable" is important because only behavior which we can measure through tests, scans, or electro-recording is behavior which we can infer is in part caused by the brain. Conclusions about the origin of abstractions like morality and love can only come from observed correlation between brain activity and the subject's overt response which we label as the abstraction, say, love. Love may or may not be solely the responsibility of the brain. Since love deals with input from the environment external to the nervous system and its expression involves behavior originating in the brain, there is some accountability of the brain for such abstractions. We could measure physiological responses of a subject who speaks of loving someone but they aren't easily distinguishable from the responses during other emotions, say, a crush on that person. It would be very difficult to show changes in the brain that directly correlate with the changes in what a subject reports is a crush to what a subject reports is love. Also, we can't know if something "spiritual" acts on the brain at some point during this process. If so, some thoughts and feelings may not be completely accountable for by the brain.
Interesting issue: are there "non-observable" aspects of behavior. Certainly in practice, at any given state of understanding/technology. But in principle? People do have trouble (for a while) distinguishing a crush from being in love, but usually get it straight eventually. Are the two initially distinguishable in terms of brain function? Or does that distinction too appear only eventually? Nice question. Presume "spiritual" also offered as an "in principle" non-observable? Let's see at the end of the course whether we still feel a need for "in principle" non-observables. PG