Proton-coupled electron transfer (PCET) is the underlying mechanism governing important reactions ranging from water splitting in photosynthesis to oxygen reduction in hydrogen fuel cells. The interplay of proton and electronic charge distribution motions can vary from sequential to concerted schemes, with elementary steps occurring on ultrafast time scales. We demonstrate with a simulation study that femtosecond soft-X-ray spectroscopy provides key insight into the PCET mechanism of a photoinduced intramolecular enol* $\rightarrow$ keto* tautomerization reaction. A full quantum treatment of electronic and nuclear dynamics of 2-(2-hydroxyphenyl-)benzothiazole upon electronic excitation reveals how spectral signatures of local excitations from core to frontier orbitals display the distinct stages of charge migration for the H atom, donating, and accepting sites. Our findings indicate UV/X-ray pump-probe spectroscopy provides a unique way to probe ultrafast electronic structure rearrangements in photoinduced chemical reactions essential to understanding the mechanism of PCET.