Haggling is essential
The truth is that although there were multiple stores in Tozeur, I couldn't find any typical product that characterised the city different to any other place. The stores are spread both in the narrow streets of Ouled el-Hadef neighborhood, as in Av Habib Bourguiba and around Ibn Chabbat. What you can find in them: Desert Roses, tunics and chilabas, wicker baskets, bowls or ceramic tiles decorated, copper kettles, carpets, jewelery in silver or alpaca, boxes of dates (perhaps most typical south of the country), and all kinds of souvenirs. As always, haggling is essential.