We present a pipeline to identify photometric variability within strong gravitationally lensing candidates, in the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys. In our first paper, we laid out our pipeline and presented seven new gravitationally lensed supernovae candidates in a retrospective search. In this companion paper, we apply a modified version of that pipeline to search for gravitationally lensed quasars. From a sample of 5807 strong lenses, we have identified 13 new gravitationally lensed quasar candidates (three of them quadruply lensed). We note that our methodology differs from most lensed quasar search algorithms that solely rely on the morphology, location, and color of the candidate systems. By also accounting for the temporal photometric variability of the posited lensed images in our search via difference imaging, we have discovered new lensed quasar candidates. While variability searches using difference imaging algorithms have been done in the past, they are typically performed over vast swathes of the sky, whereas we specifically target strong gravitationally lensed candidates. We also have applied our pipeline to 655 known gravitationally lensed quasar candidates from past lensed quasar searches, of which we identified 13 that display significant variability (one of them quadruply lensed). This pipeline demonstrates a promising search strategy to discover gravitationally lensed quasars in other existing and upcoming surveys.
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