We consider an axially elongated (or stretched) cholesteric elastomer, prolate or oblate, containing a spaceless twist defect. We show that the wavelength of its localized mode can be tuned by either axially compressing (or enlarging) the elastomer or by changing its pitch. We calculate the dwell time given by the inverse relative line width and exhibit that it is enhanced when the values of the deformation and pitch are near a locus in the parameter's sample that we call the pseudo-isotropic curve. We also show the density of states diverges in the pseudo-isotropic curve.