Giovannini Mirror Syndrome is not thought to be a real syndrome.
It has occurred only twice in real life and is thought to be because someone has incured severe brain damage, causing no understanding of the person's self to be retained. Therefore they use other people's moral compass and ideals to form a basis for themselves.
A doctor who sees someone with Giovannini Mirror Syndrome will see that the person with the mirror Syndrome will copy the profession of the doctor. House's team dealt with a patient who exhibited symptoms in the episode Mirror Mirror.
Let us not forget how the subject copies who they figure to be the more authoritive if there are more than one subject from which to copy. See the last interaction between the patient, House, and Cuddy.