Technically speaking, these aren't cooldowns. When you pull those levers the map changes "permanently". But they'll appear again when there's a floor reset in the area. Floor resets usually happens every 6-8 hours, but not at the same time on all places, and are also not related to players' actions (but they won't happen if there's a player in the area). So to answer your question, you would have to pull a lever and then check that spot as often as possible, without staying in that area, until you can narrow it down to a time span and double check it afterwards. It's not very pratical and tbh not really worth it imho.