The evolution of the scanning modules for scanning transmission electron microscopes (STEM) has realized the possibility to generate arbitrary scan pathways, an approach currently explored to improve acquisition speed and to reduce electron dose effects. In this work, we present the implementation of a random scan operating mode in STEM achieved at the hardware level via a custom scan control module. A pre-defined pattern with fully shuffled raster order is used to sample the entire region of interest. Subsampled random sparse images can then be extracted at successive time frames, to which suitable image reconstruction techniques can be applied. With respect to the conventional raster scan mode, this method permits to limit dose accumulation effects, but also to decouple the spatial and temporal information in hyperspectral images. We provide some proofs of concept of the flexibility of the random scan operating mode, presenting examples of its applications in different spectro-microscopy contexts: atomically-resolved elemental maps with electron energy loss spectroscopy and nanoscale-cathodoluminescence spectrum images. By employing adapted post-processing tools, it is demonstrated that the method allows to precisely track and correct for sample instabilities and to follow spectral diffusion with a high spatial localization.