I was thinking maybe more something like “actor” - actor might mean anyone who acts, or it might mean specifically a male actor, depending on if the person talking is also going to use “actress” or not.
To me that’s what the Wikipedia article makes it sound like -
両方の意味で使われる言葉として雇用者 ← mentioning it on its own as an example that could be used for either employer or employee,
雇用者・雇用主のペア ← using it as the opposite of 雇用主 (unambiguously employer) to mean “employee” specifically
雇用者 is probably mainly used to mean “employee” but formally it’s not definitely that side of the coin the way 雇用主 definitely means employer - in perhaps the same way “actor” is sometimes gendered but isn’t definitely gendered the way actress is.
… if that comparison makes sense anyway.
I would speculate it might come across as less weird in dictionaries if English had a word for a nonspecific party in an employee/employer relationship. Then, perhaps, the dictionary definitions would read “the specific word + the general word” rather than “specific word X + opposite word Y”
EDIT: on the other hand, Weblio gives:
こよう‐しゃ【雇用者】
１ 労働者を雇っている個人や企業などの組織。使用者2のこと。雇用主。
２ 企業・団体・個人事業主などに雇われている人。被雇用者。被用者。
Which seems like pretty much just “1. Employer 2. Employee” to me. So… there’s that.
Likely ultimately it has to do with the Chinese roots of the compoud as Jonapedia talked about in the thread I linked: