The invisible timer is both invisible and random - from my understanding it can take anything between 6 and 48 hours (though we dont know the precise times - could even be less or even more).
The point of this timer is that no one knows when it will end - once the plot goes up for sale, the invisible timer starts ticking. In order to give everyone a "fair chance" at it, its also random. (Dont tell me that that isnt fair or a stupid system, I did not put it in place.)
The reason behind this is that we used to have a huge problem with house flipping: People would buy plots with the sole intention of selling them off later. In order to do so, the seller and buyer would agree on a price for the house (often way, way more than the plot itself costs) and once gil exchanged hands, the seller would relinquish the plot so that the buyer could snatch it right up. To combat that, they put the invisible, random timer in place - both it being invisible and random play a role in the combat against house flipping (if it was only invisible but with a set time, people would have figured out what that timer was and would be able to plan for it; if it was only random but visible you could again plan for it - in that case everyone would show up within the last few minutes of the timer aswell, not giving anyone a better chance to get the house).
The relocation feature bypasses the timer btw - so you could always buy a house in a less desirable spot and relocate freely to any open house you want.
At the current time the timer is not a great feature, but one that is needed until the underlying problem is solved one way or another. All suggestions in order to change this timer are usually not thought all the way through and are mostly made with the idea in midn how much easier it would be for oneself to buy the house - without considering that it would also be that much easier for everyone else and there chances of getting the house in the first place would most likely go down, not up.