Look, GPs - you likely don't do this (and it irks patients that you don't)
Eye contact is one of the most basic mammalian traits that signals an interaction. Anybody who has a dog or cat at home sees on a daily basis how much animals value eye contact (and with dogs, it signals you’ve lost the battle!).
In the case of healthcare, during frequent emotional exchanges between two human beings, it naturally follows then that simple eye contact has to be at the core of the doctor-patient interaction.