Everything I've read says to start taking it 5 days before you are going to ovulate. But I dont know how that works since you said you arent sure of when.
I believe I've read it's unwise to take throughout the entire cycle. Do you not know when you ovulate because you're irregular, or because you haven't done temps or opks yet? If it's because you're irregular, can you ballpark it within a week and try mucinex in that timeframe? Ttc concerns aside, it's probably not wise to take any medication more than necessary, best to try narrowing the time frame down.