Since 2013, the four sites of the Fluorescence Detector (FD) of the Pierre Auger Observatory have been recording transient luminous events called ELVES with a dedicated trigger. These light emissions are correlated to distant lightning strikes. The length of recorded traces has been increased from 100 μs (2013), to 300 μs (2014-16) and to 900 μs (2017-present), to better calculate the total energy of the UV light emitted at the base of the ionosphere and its angular distribution above the lightning strike. The reconstruction of the time evolution of the light front allows an accurate determination of the lightning bolt location, within a few kilometers, as confirmed by the comparison with ground-based lightning detection networks. The time resolution of the FD applied to the observation of ELVES is a novel approach to probe fundamental physics in thunderstorms such as their charge distribution and lightning initiation processes. Argentina has been flagged as one of the most active regions on Earth for the most extreme lightning strikes, which highlighted the serendipitous opportunity the Auger Observatory is offering to the geophysics community.