We study the pseudospin and spin dynamical effects in single-layer silicene due to a perpendicular electric field periodically driven and its interplay with the intrinsic and extrinsic (Rashba) spin-orbit interaction. We find that the spin nonconserving processes of the real spin of the quasiparticles in silicene, induced by the rather weak spin-orbit mechanisms, manifest themselves as shifts of the resonances of its quasienergy spectrum in the low coupling regime to the driving field. We show that there is an interesting cooperative effect among the, in principle, competing Rashba and intrinsic spin-orbit contributions. This is explicitly illustrated by exact and approximated analytical solutions of the dynamical equations. In addition, we show that a finite Rashba spin-orbit interaction is indeed necessary in order to achieve a nonvanishing spin polarization. As additional feature, trivial and nontrivial topological phases might be distinguished from each other as fast or slow dynamical fluctuations of the spin polarization. We mention the possible experimental detection schemes of our theoretical results and their relevance in new practical implementation of periodically driven interactions in silicene physics and related two-dimensional systems.