Computer simulations and computational diagnostics are used to study a Monte Carlo Brownian walker moving through a glass of immobile force centers. Clear evidence for distinct trapping, hopping, and hindered-diffusive regimes is seen in the mean-square displacement and the probability distribution P(r,t) for a step r during delay t. In the hopping regime distinct time scales for intratrap and intertrap motion are apparent; probe localization and time scale separation depend inversely on temperature T. In the hindered-diffusion regime, the effective diffusion coefficient (D) over bar follows an Arrhenius temperature dependence. In this regime, [r(2)(t)] is very nearly linear in t, even for walkers that have only diffused a small fraction of the matrix particle nearest-neighbor distance. We infer that analytic calculations using relatively low-order time expansions should give reasonable values for (D) over bar of probe particles in our glass.