Temperature gradients induce mass separation in mixtures in a process called thermodiffusion and quantified by the Soret coefficient. The existence of minima in the Soret coefficient of aqueous solutions at specific salt concentrations was controversial until fairly recently, where a combination of experiments and simulations provided evidence for the existence of this physical phenomenon. However, the physical origin of the minima and more importantly its generality, e.g. in non-aqueous liquid mixtures, is still an outstanding question. Here, we report the existence of a minimum in liquid mixtures of non-polar liquids modelled as Lennard-Jones mixtures, demonstrating the generality of minima in the Soret coefficient. The minimum originates from a coincident minimum in the thermodynamic factor, and hence denotes a maximization of non-ideality mixing conditions. We rationalize the microscopic origin of this effect in terms of the atomic coordination structure of the mixtures.