Tozeur looks different from the rest of Tunisia, and the difference is brick. The old quarter, Ouled el Hadef, is built from small clay bricks fired in kilns that burn palm fronds, and the masons set some proud of the wall in zigzags, palm trees and camel train chevrons. The town grew rich on caravans: Ibn Khaldun wrote that about a thousand camels left it every day. Today the money is in dates, and the oasis holds around 400,000 palms.
Three days is the right length. Tozeur is small, and one day covers the medina, the palm grove and the museums. A second day goes to the mountain oases of Chebika, Tamerza and Mides, and a third to the salt lake, Nefta and the Star Wars set, where the desert starts. Two honest caveats: the Star Wars set is real but fading under the dunes, and the mountain oases sit within a few kilometers of the Algerian border, which some governments' advice covers. Both are explained in the plan.
Day one is Tozeur on foot, bike or cart, day two the 4x4 day trip, day three the Chott el Jerid at sunrise, Nefta and the dunes at dusk. No weekday is a hard constraint, which is rare. If you fly in, the Tunis flights run only a few days a week, so book the flight first and start the day you land. Pair it with 5 Days in Djerba and read about the country on the Tunisia page.