This paper proposes a novel method for the optimal parameter selection of the discrete-time switch model used in circuit solvers that adopt the fixed admittance matrix nodal method (FAMNM) approach. As known, FAMNM-based circuit solvers allow to reach efficient computation times, in particular for real-time simulation applications, since they do not need the inversion of the circuit nodal admittance matrix. However, these solvers need to optimally tune the so-called discrete switch conductance, since this parameter might largely affect the simulations accuracy. Within this context, we propose a method for the determination of the discrete-time switch conductance which is obtained by minimizing the distance between the eigenvalues of the original circuit's nodal admittance matrix with those associated with the circuit including the discrete-time switches. The method is proven to provide values of the discrete-time switch conductance that maximize the simulation accuracy and minimize the losses on this artificially introduced parameter. Additionally, the proposed method avoids the use of trial-and-error process typically required when discrete-time switch conductances need to be addressed in FAMNM approach. The performances of the proposed method are demonstrated for circuits with single and multiple switches in which passive RLC elements and transmission lines are both considered.