In this study we experimentally explore how the phenomenon of Coulomb drag and crosstalk can be used to probe the size of charge-density fluctuations and coupling mechanisms of Anderson insulators. We study a doped amorphous semiconductor (silicon-niobium), which from conventional transport measurements is understood to be a Coulomb glass at low dopant concentrations. Calculations and experimental results are presented for the linear-response Coulomb drag coefficients when one or both layers consist of various insulating states. It is found that the screening properties only become weak enough for accurate analysis when the material is deep in the insulating phase, and a linear-response transresistance is only obtainable over a very narrow range of experimental parameters. We uncover an additional regime that becomes dominant at higher driving-currents in which the Coulomb drag coefficient is negative at the lowest temperatures probed. We also present results for the non-linear dependence of the induced field at low driving currents in the silicon-niobium layers of certain bilayer samples. We suggest that this is related to the extended non-linearity range of the Coulomb drag coefficients with respect to the driving current.