If by 'personality and character' you mean the general patters of behavior, emotional responses and thinking that are independent of sensory input from an organisms particular surroundings, then of course yes. Those functions are widely believed to reside in the brain. From the more dualistic stand point that there may be any additional substance you could hypothesize to reside everywhere. However, the explanatory power of this theory will be very limited. All scientific evidence points to the brain.
Both of these are definitely located in the brain. Where else would they be? Sure you can have all of these things do make an impact on you and your personality, That's obvious. What people aren't really realizing is these processes still occur in the brain even after they had been influenced by another source.
We do not process information with out toes. We do not formulate thoughts with out kneecaps.
We have one large, extensive organ to receive sensory data, we have two squishy organs for visual sensory data, we have a few holes for vibration sensory data, and a few more for flavor data.
We have one organ to process the data. Our big, beautiful brains.
If there is such a thing as a human soul, it is the brain.
Everything that makes you what you are has been developed from your brain. A blend of millions of moments when your environment interacts with your genetic predisposition and forms the unique fingerprint that is your person.
When a person suffers brain damage, that person can have a dramatic shift in personality. They can essentially become a completely different person, all from something as simply as a knock to the head. These people can forget names of loved ones, common knowledge, hate things they used to love, or vice versa.
To suggest there's some sort of external working order to who you are seems to contradict this evidence.
There are many social forces that impact your personality. Your sex, gender, sexual orientation, race, ethnicity, culture, social status, and general life experiences all impact your personality, character, and world view. It's called intersectionality. For example, a person who has general trust and faith in humanity may leave their doors unlocked during the day. However, if they come home and find out they've been burglarized, this can cause a dramatic shift in their personality. They may become much more protective over their materials and lose their trust in the people surrounding them. This is just one example, there are many more.
That would primarily be the brain but anything including random quantum fluctuations that would have effects even tiny effects that would become part of the calculations and add up would have influences on personality and character. So it's not just the brain.
And a caveat needs to be made. When people say "the brain" listeners often automatically assume factors like genetics or nutrition. We need to stop and remember that social influence is in the brain too. Sound waves and light waves come into the brain and get categorized and interpreted. Hence social influence works through the brain. Talking to other people changes your worldview and hence your brain.
And so does thinking as thoughts are communications between parts of the brain and hence how you think will be equivalent to changes in your brain. Taking responsibility for how you think will generally lead to better outcomes for your brain, acting like you are helpless will lead to worse outcomes.
It sounds profound but paradoxically the most profound thing is how unprofound it is. "result of the totality of physical effects" is the same as saying that personality and character are the result of everything that interact together to create personality and character. It's very obvious once you really think about it, but has to be put in these words because it can't be reduced further not without ignoring a whole swath of factors.