  (Ultra)light spin-$1$ particles -- dark photons -- can constitute all of dark
matter (DM) and have beyond Standard Model couplings. This can lead to a
coherent, oscillatory signature in terrestrial detectors that depends on the
coupling strength. We provide a signal analysis and statistical framework for
inferring the properties of such DM by taking into account (i) the stochastic
and (ii) the vector nature of the underlying field, along with (iii) the
effects due to the Earth's rotation. Owing to equipartition, on time scales
shorter than the coherence time the DM field vector typically traces out a
fixed ellipse. Taking this ellipse and the rotation of the Earth into account,
we highlight a distinctive three-peak signal in Fourier space that can be used
to constrain DM coupling strengths. Accounting for all three peaks, we derive
latitude-independent constraints on such DM couplings, unlike those stemming
from single-peak studies. We apply our framework to the search for ultralight
$B - L$ DM using optomechanical sensors, demonstrating the ability to delve
into previously unprobed regions of this DM candidate's parameter space.
