We suggest that an interplay between microscopic and macroscopic physics can
give rise to dark matter (DM) whose interactions with the visible sector
fundamentally undulate in time, independent of celestial dynamics. A concrete
example is provided by fermionic DM with an electric dipole moment (EDM)
sourced by an oscillating axion-like field, resulting in undulations in the
scattering rate. The discovery potential of light DM searches can be enhanced
by additionally searching for undulating scattering rates, especially in
detection regions where background rates are large and difficult to estimate,
such as for DM masses in the vicinity of 1 MeV where DM-electron scattering
dominantly populates the single electron bin. An undulating signal could also
reveal precious dark sector information after discovery. In this regard we
emphasise that, if the recent XENON1T excess of events is due to light DM
scattering exothermically off electrons, future analyses of the time-dependence
of events could offer clues as to the microscopic origins of the putative
signal