If the random timer wasn't here, the previous owner would have known the exact moment when the house would be available again for purchase, and would have warned one of his friend to stay next to the plot to snatch it right away when it becomes free. Or worse, instead of giving it to a friend he could have sold it for millions of gils, or even real money to the highest bidder (this is called house flipping).
And you would have never get it.
While the invisible timer is for sure an irritating system, at least now you can SEE free plots, and even TRY to get them. Which is a huge improvement compared to the old times when house flipping was rampant without the invisible timer, and 100% of the plots always taken.
As far as i know the timer is totally random, which would be logical because it is the point of it. And if you are talking of the tiny FC room you buy for 300 000 gils, it isn't gonna work. It is the entire FC house that needs to move.
