In microfluidic applications it has been observed that flows with spatial gradients in electrical conductivity are unstable under the application of sufficiently strong electric fields. These electrohydrodynamic instabilities can drive a nonlinear flow despite the low Reynolds number. Such flows hold promise as a simple mechanism for mixing fluids. In this work, the effect of a time periodic electric field on the instability is explored. The case where an electric field is applied across a diffuse interface of two fluids with varying electrical conductivity is considered. Frequency-dependent behavior is found only in the regime where the instability growth rates are very slow and cannot outpace mixing by molecular diffusion. Improving mixing by modulation of the electric body force is not a viable strategy in this geometry.