This paper reports our simulations of the volume emission rate (VER) of the O($^1D$) redline nightglow perturbed by waves traveling across the thermosphere at around 250 km altitude. Waves perturb the electronic and neutral background densities and temperatures in the region and modify the O($^1D$) layer intensity as it is captured by ground-based nightglow instruments. The changes in the integrated volume emission rate are calculated for various vertical wavelengths of the perturbations. We demonstrate that, as the solar activity intensifies, the vertical scales of most likely observable TID waves become larger. For high solar activity, we demonstrate that only waves presenting vertical wavelengths larger than 360 km are likely to be observed. The variation of the range of likely observable vertical wavelengths with the solar cycle offers a plausible explanation for the low occurrence rate of TID in measurements of the redline nightglow during high solar activity periods. We have compared our results with those of \citeA{Negale:2018} and \citeA{Paulino:2018} to verify that observed vertical wavelengths distribute around 140-210 km, in good correspondence with our predicted threshold wavelength $\lambda_{z}^t\sim$160 km for very low solar cycle period.