We present a rigorous and comprehensive classification of the asymptotic behavior of time-dependent Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equations under the assumption of Hermitian jump operators. Our results apply to a broad class of GKSL equations whose time dependence is assumed to be recurrent, including time-independent, periodic, quasiperiodic, and certain classes of random time dependence. Our main contributions are twofold: first, we establish a criterion for the uniqueness of steady states in terms of the algebra generated by the GKSL generators, which provides a necessary and sufficient condition when the generators are analytic functions of time. Second, we extend the concept of strong symmetry for time-dependent GKSL equations by introducing two distinct forms, strong symmetry in the Schr"odinger picture and that in the interaction picture, and completely classify the asymptotic dynamics with them. More concretely, we uncover that the strong symmetry in the Schr"odinger and interaction pictures is responsible for non-trivial time-independent and time-dependent steady states, respectively. This classification reveals symmetry-predicted, time-dependent asymptotic dynamics in a novel class of open quantum systems. Our framework thus provides a foundation for controlling dissipative quantum systems in a time-dependent manner.