Are there are FAA publications that state the exact definition of “inoperative equipment?”

Long story short I work at a flight school where an aircraft has an oil temp gauge that always reads high because “that’s just how it is. The A&P said so”.

I’m not looking for a “you’re the pilot in command answer”… more specifically are there any publications that DEFINE what operative means? Just because a gauge is functional does that mean it’s operative? Does the FAA intentionally leave “operative” vague?

Thanks!