Prices do fluctuate but don't expect to get lucky. What works for me is to book early (to assure that I get the stateroom that I want), continually watch for price drops or added Voyager's Club discounts, and decide if it is worth the gamble to reprice if the new price is lower. I generally book 1-2 years out so I usually end up with a good price until YC is sold out or my stateroom category is sold out.
By the time that final payment comes, there may be a few available staterooms but those might go to people who upgrade. On my next cruise, there is only 1 YC stateroom available but the price is currently higher than it was when I booked. Even though I'm past final payment date, there's no lucky/lower price way to get into the Yacht Club for someone who's looking to book.