  We have studied the low-frequency dynamics of the charge carriers in
different organic charge-transfer salts $\kappa$-(BEDT-TTF)$_2$X with polymeric
anions X by using resistance noise spectroscopy. Our aim is to investigate the
structural, glass-like transition caused by the conformational degrees of
freedom of the BEDT-TTF molecules' terminal ethylene groups. Although of
fundamental importance for studies of the electronic ground-state properties,
the phenomenology of the glassy dynamics is only scarcely investigated and its
origin is not understood. Our systematic studies of fluctuation spectroscopy of
various different compounds reveal a universal, pronounced maximum in the
resistance noise power spectral density related to the glass transition. The
energy scale of this precess can be identified with the activation energy of
the glass-like ethylene endgroup structural dynamics as determined from
thermodynamic and NMR measurements. For the first time for this class of
'plastic crystals', we report a typical glassy property of the relaxation time,
namely a Vogel-Fulcher-Tammann law, and are able to determine the degree of
fragility of the glassy system. Supporting $\textit{ab initio}$ calculations
provide an explanation for the origin and phenomenology of the glassy dynamics
in different systems in terms of a simple two-level model, where the relevant
energy scales are determined by the coupling of the ethylene endgroups to the
anions.
