It shouldn't go dead, there's a Power Saver circuit inside the BCM that should turn off power to all the courtesy lights if they've been lit for some extended period (15~20 minutes on most Nissan products). The Power Saver gets reset whenever you close and reopen a door. The dim lights are most likely from the welcome effect I mentioned, and if they're going out after a short time then it sounds like they're working normally. They shouldn't be staying lit, which was what I inferred from your first post. According to the manual, the behaviors are a bit different for the driver's door and depending whether there's an I-key in range of the receivers in the outside front door handles.
Maybe the previous owner was a dope dealer and had a problem with his courtesy lamps working for customers. I dunno.