We consider Spin(4)-equivariant dimensional reduction of Yang Mills theory on manifolds of the form M-d x T-1,T-1, where M-d is a smooth manifold and T-1,T-1 is a five-dimensional Sasaki Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on M-d extending those induced via reduction over the leaf spaces CP1 x CP1 in T-1,T-1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin(4)-equivariant instantons on the conifold which is realized as the metric cone over T-1,T-1. We give an explicit construction of these moduli spaces as Kahler quotients. (C) 2016 The Authors. Published by Elsevier B.V.