We begin the search for extremely-low mass ($Mleq0.3M_{odot}$, ELM) white dwarfs (WDs) in the southern sky based on photometry from the VST ATLAS and SkyMapper surveys. We use a similar color-selection method as the Hypervelocity star survey. We switched to an astrometric selection once Gaia Data Release 2 became available. We use the previously known sample of ELM white dwarfs to demonstrate that these objects occupy a unique parameter space in parallax and magnitude. We use the SOAR 4.1m telescope to test the Gaia-based selection, and identify more than two dozen low-mass white dwarfs, including 6 new ELM white dwarf binaries with periods as short as 2 h. The better efficiency of the Gaia-based selection enables us to extend the ELM Survey footprint to the southern sky. We confirm one of our candidates, J0500$-$0930, to become the brightest ($G=12.6$ mag) and closest ($d=72$ pc) ELM white dwarf binary currently known. Remarkably, the Transiting Exoplanet Survey Satellite (TESS) full-frame imaging data on this system reveals low-level ($<0.1$%) but significant variability at the orbital period of this system ($P=9.5$ h), likely from the relativistic beaming effect. TESS data on another system, J0642$-$5605, reveals ellipsoidal variations due to a tidally distorted ELM WD. These demonstrate the power of TESS full-frame images in confirming the orbital periods of relatively bright compact object binaries.
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