The High Elevation Auger Telescopes (HEAT) has increased the Field of View (FoV) of the Fluorescence Detector (FD) at the Coihueco site of the Pierre Auger Observatory and allowed the extension of the energy threshold for the measurements of energies and $X_{\textrm{max}}$ of Extensive Air Showers (EAS) down to $\approx10^{17.2}$ eV. By temporarily orienting HEAT in the downward position, it acquires data in the same FoV as the other Coihueco telescopes, thus providing the opportunity to intercalibrate the detectors by multiple observations of the same EAS. To further control systematic uncertainties in $X_{\textrm{max}}$ and energy measurements, in this contribution we present an innovative method that takes advantage of the Night Sky Brightness (NSB) continuously measured with the FD data acquisition system for monitoring a possible evolution in time of the initial HEAT and Coihueco inter-calibration. While the brightness of the night sky evolves unpredictably and is highly dependent on local weather conditions, we expect to obtain consistent measurements from telescopes located at the same site and observing the same direction of the sky. In this work, we describe the method used to compare the NSB measured by the neighboring HEAT and Coihueco telescopes to monitor the stability of their relative calibration over time. This method allows us to study further the systematics in the inter-calibration of the FD telescopes.