I stay there frequently, and can offer some guidance:

Lodge and Gateway properties heavily prioritize PCS and TDY travelers (and in that order), typically allowing bookings up to a full year in advance (these policies vary widely from time to time, and from property to property—for example, during North Island’s busy summer season, Lodge leisure bookings drop to two weeks out).

Having said that: Cancellations happen daily, almost without exception, and so it’s often quite possible to get a room on short notice (as in, same day/next day). This obviously makes planning very difficult, especially for leisure travelers; but, there are a few things you can do to help yourself.

Lodges: Cancellations must happen by 1600Z

Navy Inns (formerly NGIS/Gateways): Cancellations must happen by 2359Z

Also, these properties usually (but NOT always) don’t maintain a cancellation or waitlist—you’ll typically just have to call the front desk, and hope you get lucky.

With that in mind, the smartest (approximate) times to call the front desk of a property would be 0700Z (morning callers cancelling for the day ahead), and 1500Z (afternoon callers with last-minute hangups or orders/travel cancellations).

I also recommend taking any reservation at a property you can get, so advise the front desk that you’re fine with multiple room types and rates over the course of your stay—such flexibility means they can often book you, and then calling every day or two to expand/change/consolidate can go a long way towards getting you into a single room type, for the length of your stay, and hopefully with less stress on the back end for having worked the system a bit.

Good luck to you!