  New experimental quantum simulation platforms have recently been implemented
with divalent atoms trapped in optical tweezer arrays with promising
performance. The second valence electron also brings new propects through the
so-called Isolated Core Excitation (ICE), however autoionization presents a
strong limitation to this use. In this study, we propose and demonstrate a new
approach to applying a sizable light shift to a Rydberg state with
close-to-resonant ICE while avoiding auto-ionization. In particular, we have
investigated ICE of ytterbium atoms in $^1S_0$ Rydberg states. Spectroscopic
studies of the induced auto-ionization and the light shift imparted to the
Rydberg states are perfectly accounted for with Multi-channel Quantum Defect
Theory. Such a control over the inner electron without disturbing the Rydberg
electron brings a new tool for the targeted, coherent manipulation of Rydberg
states in quantum simulation experiments performed with alkaline-earth atoms.
