I personally have not heard of anyone getting a "last minute" cruise anymore. security has become very strict sine 9/11.
I was under the impression the cruise lines needed 24 hours to finalize the manifest before the ship sailed, and I have not had anyone tell me they booked the same day since before 2001.
That manifest is taken very seriously and the FBI has arrested several people who came up as being wanted as a result of scrutinizing that manifest (they have all been arrested coming off the ship, however, not before getting onboard).
I am not a travel agent, so I do not know when the window closes. But it is not something I really care much about anyway since a cruise is a pretty significant investment and most people like to plan them out well in advance.
See, people who think a cruise line will sell a cheap cabin at any price at the last minute rather than let it go empty are missing the big picture.
The cruise lines are not stupid about public perception - they manage their "booking window" very carefully. The last thing they would ever do is admit that there are (literal) last minute bargains available on cruises. Their goal is to move bookings out as far as possible so they have visibility on their future income.
They do all they can to incentivize people to book 6 to 12 months out.
A cruise ship will often get cheaper right after final payment is due (60-75 days out) - but as a ship fills up, it can actually become far more expensive at the last minute - even if there are empty cabins. This is because they know that anyone who wants to be on that cruise at the last minute has a reason for it (to join a friend or family onboard, for example) and so they will pay more to go.
Only if a ship is VERY empty will you see it get very cheap within the last two weeks before it sails. Alaska cruises in May when the region is over-capacity are sometimes like this, but not much else.
I only said what I said (about berth capacity, etc. above) to let people know that what the cruise lines say about all sailings being full is not entirely accurate - however, they may as well be full as far as cruise line policy is concerned. The line will act as if the ship is full, even if there are empty spaces. Will they put name tags on doors? I doubt that.
And in fact - most cabins are probably full on most sailings. I have been on many sailings where it was obvious the ship was well over berth capacity. As I said, Disney typically sells 95% full including third & fourth beds.
A Celebrity cruise will have very few kids onboard, so it may be less full, but almost every cabin may be inhabited.
I am sorry if this does not answer your question. All I am trying to say is that cruise lines are not transparent about these matters. They guard such information very carefully, and that has been a very successful approach for them.