The exact condition is: (1) collect at least 50 information and (2) it has to be nighttime (night or late night). When you meet those conditions, just entering the brothel or returning to the lobby after sleeping with a customer, will cause the event unlocking the backroom to trigger automatically. You can’t really see how much information you have, but 50 isn’t a ton, really. While it is possible to get no information from a customer, the minimum you get when you do find information is like 10 or so, and some people can drop like 20+ information.