The process is largely controlled by computer software and is increasingly being bolstered by AI, so price changes can happen at any second. That's why there's no specific time of day — or even a specific day of the week, for that matter — that's best for booking cheap flights.
Why do flight prices go up and down every day?
Although the general trend is for flights to get more expensive as time goes by and more seats are sold, from time to time the airlines will make adjustments and release more seats at the lower buckets. This is why fares sometimes move down, as well as up, even without an explicit fare decrease by the airline.