ASTRI-Horn is the Cherenkov telescope developed by INAF and operating in Italy on the slopes of Etna volcano. Characterized by a dual-mirror optical system and a focal plane covered by silicon photomultiplier sensors, ASTRI-Horn is a prototype of the telescopes proposed to form one of the pathfinder sub-arrays of the Cherenkov Telescope Array Observatory in Chile. The electronics of the ASTRI-Horn telescope, optimized to detect nanosecond burst of light, is not able to directly measure any continuous or slowly varying flux illuminating its camera. To measure the intensity of the night sky background (NSB) in the field of view of the telescope, the firmware of the ASTRI-Horn camera continuously performs the statistical analysis of its detector signals and periodically provides in output the "variance" of each pixel, which is linearly dependent on the rate of detected photons; in this way, an indirect, but accurate measurement of the NSB flux is obtained without interference with the normal telescope operation. In this contribution we provide an overview of several calibration and monitoring tasks that can be performed in a straightforward way by the analysis of the "variance" data such as the camera astrometry, the actual telescope orientation and the monitoring of its optical point spread function.