The idea that the duration of the trip due to budget determines the low season doesn't necessarily hold, the old playbook teaches us flexibility.
Previous says: we've always managed with what we have here, and if the budget only allows two weeks, we first look for the best offers for that duration, regardless of the season.
You can very well find interesting promotions in peak season or cheaper destinations, like a quick stay in Hammamet during summer, to stay within your budget.
Having a tight budget doesn't automatically impose the low season; it mainly encourages being smart and seeking the best opportunities for the time available.