What is an agent noun?
Agents generally have the endings “-er” or “-or.” These suffixes, when added to a root word, mean someone who does something.
OP:
Not quite. The word I'm looking for would be used to refer to a person who mirrors others in speech and action. If that definition of mirrorer is used enough, then perhaps an agent noun of mirror cannot exist. In any case, thanks for sharing it here!
Answer
I think you mean “mirrorizer” but it’s not an actual word as far as I’m aware that’s in a dictionary. It’s from the verb mirrorize (obsolete; rare according to OED) + the ending -er (where the extra e is dropped).
It’s the same with other agent nouns that end with e for example:
hypnotize + er = hypnotizer
https://en.m.wiktionary.org/wiki/hypnotizer
mesmerize + er = mesmerizer