How much brain do the Cicada fungus "zombies" have?
www.nationalgeographic.com
I am also now imagining a potential other case where the outbreak is embarrassingly at a necromancers, where they're mixed in with the regular zombies - and where we can imagine a reason why the two kinds have no interest in each other.

This fungus turns cicadas into zombies who procreate until they die
Massospora consumes cicadas from the inside out then drives them to mate—in the process making infected males more attractive to both sexes.
I am also now imagining a potential other case where the outbreak is embarrassingly at a necromancers, where they're mixed in with the regular zombies - and where we can imagine a reason why the two kinds have no interest in each other.