The answer is “Governor.” The Constitution never refers to the Governor of a State. The phrases used instead are “executive authority” or “executive officer.” I’m not sure why. One possible answer is that at least one state in 1787 did not have a Governor, but instead relied on some form of collective executive. (I still need to research that.)
This textual point sheds some light on the Supreme Court’s upcoming examination of what the word “Legislature” means in the Arizona redistricting case. The Constitution does refer specifically to the Legislature (rather than to “the Legislature authority”) in many places, which suggests that the Legislature itself must play a significant role in the tasks that are delegated to it by the text. The Arizona Constitution does not do that with respect to redistricting, which is why I’m sticking with my view (after initially concluding otherwise) that the constitutional challenge by the State Legislature should succeed.
UPDATE: Vik Amar has a new column arguing that an Act of Congress authorizes what the Arizona Constitution does. It’s an interesting take that might lead me to change my mind again. After all, Article 1, Section 4 gives Congress given broad authority over districting if it chooses to exercise that power.