We investigate the low-frequency charge-carrier dynamics of a molecular dimer-Mott insulator β′-(BEDT-TTF)2ICl2, where the freezing of charge fluctuations on the dimers gives rise to electronic ferroelectricity. We show that conductance fluctuation (noise) spectroscopy allows one to probe changes in the dielectric properties at elevated temperatures, where samples are even still in the conductive regime. Our results explain the formation of electric polarization states leading to glassy and relaxor-type ferroelectric behavior that is frequently observed in these systems. The onset of distinct two-level fluctuations and changes of the underlying 1/f-type noise indicate the formation of nanoscale polar regions, the dynamics of which depends on the applied electric fields. Conductance noise spectroscopy therefore is a suitable tool for investigating the onset of electric-polarization dynamics in molecular and other, inorganic charge-driven ferroelectrics.