In cryogenic ion vibrational predissociation (CIVP) spectroscopy, the influence of the tag on the spectrum is an important consideration. Whereas for small ions several studies have shown that the tag effects can be significant, these effects are less understood for large ions or for large numbers of tags. Nevertheless, it is commonly assumed that if the investigated molecular ion is large enough, the perturbations arising from the tag are small and can therefore be neglected in the interpretation. In addition, it is generally assumed that the more weakly bound the tag is, the less it perturbs the CIVP spectrum. Under these assumptions, CIVP spectra are claimed to be effectively IR absorption spectra of the free molecular ion. Having observed unexpected splittings in otherwise unproblematic CIVP spectra of some tagged ions, we report Born-Oppenheimer molecular dynamics (BOMD) simulations that strongly indicate that mobility among the more weakly bound tags leads to the surprising splittings. We compared the behavior of two tags commonly used in CIVP spectroscopy (H-2 and N-2) with a large pyridinium cation. Our experimental results surprisingly show that under the appropriate circumstances, the more weakly bound tag can perturb the CIVP spectra more than the more strongly bound tag by not just shifting but also splitting the observed bands. The more weakly bound tag had significant residence times at several spectroscopically distinct sites on the molecular ion. This indicates that the weakly bound tag is likely to sample several binding sites in the experiment, some of which involve interaction with the reporter chromophore.