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Triangular lattice delafossite compounds built from magnetic lanthanide ions are a topic of recent interest due to their frustrated magnetism and realization of quantum disordered magnetic ground states. Here we report the evolution of the structure and electronic ground states of RbCe$X_2$ compounds, built from a triangular lattice of Ce$^{3+}$ ions, upon varying their anion character ($X_2$= O$_2$, S$_2$, SeS, Se$_2$, TeSe, Te$_2$). This includes the discovery of a new member of this series, RbCeO$_2$, that potentially realizes a quantum disordered ground state analogous to NaYbO$_2$. Magnetization and susceptibility measurements reveal that all compounds manifest mean-field antiferromagnetic interactions and, with the exception of the oxide, possess signatures of magnetic correlations onset below 1 K. The crystalline electric field level scheme is explored via neutron scattering and \textit{ab initio} calculations in order to model the intramultiplet splitting of the $J=5/2$ multiplet. In addition to the two excited doublets expected within the $J=5/2$ manifold, we observe one extra, local mode present across the sample series. This added mode shifts downward in energy with increasing anion mass and decreasing crystal field strength, suggesting a long-lived anomalous mode endemic to anion motion about the Ce$^{3+}$ sites.