We analyze the Markovian and non-Markovian stochastic quantization methods for a complex action quantum mechanical model analog to Maxwell-Chern-Simons electrodynamics in Weyl gauge. We show through analytical methods convergence to the correct equilibrium state for both methods. Introduction of a memory kernel generates a non-Markovian process which has the effect of slowing down oscillations that arise in the Langevin-time evolution towards equilibrium of complex-action problems. This feature of non-Markovian stochastic quantization might be beneficial in large-scale numerical simulations of complex action field theories on a lattice.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)