This paper deals with linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated anisotropic Brinkman porous layer subject to the combined effect of AC electric field and time-periodic gravity modulation (GM). In the realm of linear theory, the critical stability parameters are computed by regular perturbation method. The local nonlinear theory based on truncated Fourier series method gives the information of convection amplitudes and heat transfer. Principle of exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system several qualitative results on stability are discussed. The sensitive dependence of the solution of Lorenz system of electrothermal convection to the choice of initial conditions points to the possibility of chaos. Low frequency g-jitter is found to have significant stabilizing influence which is in turn diminished by an imposed AC electric field. The role of other governing parameters on the stability threshold and on transient heat transfer is determined.