Even though I mostly agree with the personality being in the mind, here are a few alternative ideas:

Hormones have a large impact on emotions, and I could be wrong but aren't some hormones produced by glands that are outside of the brain?

The stereotype that women have about men is that at least part of their thinking is controlled by a part of their anatomy below their waist. it's a stereotype, but stereotypes may have some basis in truth.

Self esteem is very linked with one's sense of one's body: whether one approves of one's body or not, whether the body is a well oiled machine or clutzy and inept, skinny and fat matter a lot to many women's self esteem. How fit one's body is determines which activities one can perform, how tired one is, etc.

I am thinking there may be other things as well. Sure, they may seem minor compared to the brain but all this adds up and has a potentially large influence on personality.