The exact Kohn–Sham (KS) system must have its highest occupied orbital energy equal to the negative of the lowest vertical ionization energy (VIE). No comparable theorem connects the deeper occupied levels εₖ to the higher VIEs Iₖ. Chong, Gritsenko and Baerends (CGB) established empirically that Iₖ + εₖ∝√(ε_HOMO-εₖ). We ask whether a similar relation holds for the exact generalized Kohn-Sham (GKS) system, which incorporates a fraction α of Hartree-Fock exchange. We invert near-exact CCSD/aug-cc-pVQZ ground-state densities of LiH, LiF, H₂O, HF, CO, N₂ and F₂ at α = 0, 0.25, 0.5, 0.75, 1.0 and obtain the exact GKS systems at each admixture. As the density is held fixed and only the operator is varied, the resulting occupied spectra separate the effect of exact-exchange admixture on orbital energies from its effect on the density, two contributions inseparable in a self-consistent hybrid calculation. The CGB relation holds broadly across the family, with a proportionality coefficient linear in α, c(α)=c(0)-sα, where c(0)=1.185±0.017 eV^(1/2) and s=1.987±0.041 eV^(1/2), with R²≥0.9996 for H₂O, CO, HF and N₂. Using the response-potential matrix elements tabulated by Gritsenko, Braïda and Baerends, we decompose the CGB coefficient into response and spectroscopic parts, and find s to agree with the homogeneous-electron-gas step-height coefficient K_g = 1.9932 eV^(1/2), which we conjecture is its origin. The coefficient vanishes at α^*=0.597±0.008. At α^* the HOMO-referenced GKS occupied levels satisfy εₖ≈-Iₖ across the whole occupied range. The zero crossing is fixed by the core orbitals; in the outer valence the CGB coefficient is already indistinguishable from zero at α=0.