We present a novel method to detect variable astrophysical objects and transient phenomena using anomalous excess scatter in repeated measurements from public catalogs of Gaia DR2 and Zwicky Transient Facility (ZTF) DR3 photometry. We first provide a generalized, all-sky proxy for variability using only Gaia DR2 photometry, calibrated to white dwarf stars. To ensure more robust candidate detection, we further employ a method combining Gaia with ZTF photometry and alerts. To demonstrate its efficacy, we apply this latter technique to a sample of roughly 12100 white dwarfs within 200pc centered on the ZZ Ceti instability strip, where hydrogen-atmosphere white dwarfs are known to pulsate. By inspecting the top 1% of the samples ranked by these methods, we demonstrate that both the Gaia-only and ZTF-informed techniques are highly effective at identifying known and new variable white dwarfs, which we verify using follow-up, high-speed photometry. We confirm variability in all 33 out of 33 (100%) observed white dwarfs within our top 1% highest-ranked candidates, both inside and outside the ZZ Ceti instability strip. In addition to dozens of new pulsating white dwarfs, we also identify five white dwarfs highly likely to show transiting planetary debris; if confirmed, these systems would more than triple the number of white dwarfs known to host transiting debris.