A detailed microscopic and quantitative description of the electronic and magnetic properties of Gd$^{3+}$-doped YCo$_{2}$Zn$_{20}$ single crystals (Y$_{1-x}$Gd$_{x}$Co$_{2}$Zn$_{20}$: (0.002 $\lesssim x \leq $ 1.00) is reported through a combination of temperature-dependent electron spin resonance (ESR), heat capacity and $dc$ magnetic susceptibility experiments, plus first-principles density functional theory (DFT) calculations. The ESR results indicate that this system features an \emph{exchange bottleneck} scenario wherein various channels for the spin-lattice relaxation mechanism of the Gd$^{3+}$ ions can be identified via exchange interactions with different types of conduction electrons at the Fermi level. Quantitative support from the other techniques allow to extract the exchange interaction parameters between the localized magnetic moments of the Gd$^{3+}$ ions and the different types of conduction electrons present at the Fermi level ($J_{fs}$, $J_{fp}$ and $J_{fd}$). Despite the complexity of the crystal structure, our combination of experimental and electronic structure data establish GdCo$_{2}$Zn$_{20}$ as a model RKKY system by predicting a Curie-Weiss temperature $\theta_{C} = -1.2(2)$~K directly from microscopic parameters, in very good agreement with the bulk value from magnetization data. The successful microscopic understanding of the electronic structure and behavior for the two end compounds YCo$_{2}$Zn$_{20}$ and GdCo$_{2}$Zn$_{20}$ means they can be used as references to help describe the more complex electronic properties of related materials.