Similarly to the action of Out(FN) on Outer Space, the outer automorphism group of a Generalized Baumslag Solitar group acts on a deformation space endowed with the Lipschitz metric and the action of any fully irreducible automorphism with a train track representative is hyperbolic. Inspired by previous work by Algom-Kfir, we prove that the axis of such an automorphism is strongly contracting.