“Are the county clerks employed by the governor?”
I am not sure if you are asking a direct question.
I would assume that the county clerks are employees indirectly of the state. Hired by the county, but the county must, by state law, follow state law, which is enforceable by the governor. Is that what you were asking?
It is true, of course, that county clerks are bound by state law. But it is not clear that they are employed by the governor. It is not clear that they are agents of the governor under the principles of the Restatement of Agency.