If it's so innate, why does the child have long hair? Is it perhaps the parents enforcing a gender role upon a child and through the interaction continue to enforce a gender role upon the child?

Sometimes it doesn't take much to really impact someone. There was a story I remember hearing about how a family had tried to raise their kids without specific gendered expectations and the son was really into something traditionally feminine. It was only after his friends came over and gave him a weird look over it that suddenly he immediately dropped the interest because he was told very clearly through the reactions of his peers that what he was doing was "wrong." I imagine the exact same thing has happened with this child. From my own personal experience, as a child I had a high pitched singing voice and one day I was singing in the car because I loved to sing and my aunt laughed and laughed and laughed at how girly I sounded. I can barely sing in front of people to this day because even after coming out as trans and realizing that it was bullshit, the experience has made me deeply uncomfortable singing near people lest they laugh at me again, though this time for having too deep of a voice I suppose.