A peculiar property of the Cartesian ego is that there can be only one of them.
I think, therefore I am. The Cartesian Ego springs into existence. My own thinking is the one indubitable fact; it is the fact in terms of which all other facts are conditioned.
What about your thinking? Unfortunately for you, while I cannot doubt the reality of my own thought, it is quite possible for me to doubt the reality of your thought. Your being, and whatever thought it might involve, is just another item in my world, a world in which all being has existence only in light of the certainty and existence of my own ego; my own I think.
Even if I condescend to grant that you go through a similar process of radical doubt and discovery of the certainty of the thinking subject, and give you the name "Cartesian Ego", I am only using the title equivocally, the way a King might grant the title "King" to a visiting potentate. You may be a King in your kingdom, but in my kingdom, you are just another person subject to my rule. And the difference between an earthly kingdom and the Cartesian Kingdom is that the Cartesian Kingdom is, by definition, co-extensive with the world. So I can't help but think of you as a king without a kingdom; my kingdom must stretch from one end of the world to the other. "This town isn't big enough for the two of us."
So when philosophers and scientists go hunting for the Cartesian ego in brain studies, Cartesian Theaters, or philosophical zombies, the situation is comical. The only place you might encounter the Cartesian Ego is in the mirror - the one place the Cartesian Ego hunters always fail to look.