Developing tissues need to pattern themselves in space and time. A prevalent mechanism to achieve this are pulsatile active stresses generated by the actin cytoskeleton. Active gel theory is a powerful tool to model the dynamics of cytoskeletal pattern formation. In theoretical models, the influence of the viscoelastic nature of the actin cytoskeleton has so far only been investigated by the incorporation of one viscoelastic relaxation time scale. Here, using a minimal model of active gel theory, we show that distinct shear and areal relaxation times are sufficient to drive pulsatile dynamics in active surfaces with only a single molecular regulator.