Understanding the strange metallic behavior that develops at the brink of localization in quantum materials requires probing the underlying electronic charge dynamics. Using synchrotron radiation-based Mössbauer spectroscopy, we studied the charge fluctuations of the strange metal phase of β-YbAlB4 as a function of temperature and pressure. We found that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. We interpret this spectrum as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time scales are further enhanced by the formation of charged polarons. These critical charge fluctuations may prove to be a distinct signature of strange metals.