This is very situational based on how the athlete feels the day the rest begins.
I also do two peaks a year (my College team views Indoor & Outdoor as one season, there is no break in training between seasons unless it is absolutely necessary) and time off is pretty important to look at, because if everything goes right, you only get to take time off twice a year.
For a person who finished the season feeling very strong, continued to improve every meet and workout, but didn't make the postseason (usually sophomores and juniors) the least time is taken off, as little as 5-6 days. Following that normal training can begin. For most athletes they will reach a new peak mileage this off season.
For a person who finished the season feeling beaten up, and didn't race or workout well as the season progressed, the most time is taken off, as much as two weeks, unless there is an injury, then more time, based on what the injury is. A slower build up is used as they return from the longer time up, they typically come back at a low mileage and spend the off season building continuously. These athletes may not make it back to their peak mileage before the season, and might use the following season to continue building mileage, with less emphasis on racing and working out, although that applies primarily for athletes with significant injuries they sustained the previous season.
For a person who ran in the postseason (Conference, Regional, National) A minimum of 7 days is usually taken off, no matter how good they feel, and the first week back is usually fairly light, as little as 50-60% of their normal mileage, from there they train the same way anyone else would, based on how they felt at the season's close.
So at one extreme, there is a kid who might not get back up to his in season mileage until some time during the next season, several months later, on the other hand, a kid might be running his mid season mileage a week after his last race.