  The $\textit{Kepler}$ satellite potentially provides the highest precision
photometry of active galactic nuclei (AGN) available to investigate
short-timescale optical variability. We targeted quasars from the Sloan Digital
Sky Survey that lie in the fields of view of the $\textit{Kepler/K2}$
campaigns. Based on those observations, we report the discovery and properties
of a previously unidentified instrumental signature in K2. Systematic errors in
K2, beyond those due to the motion of the detector, plague our AGN and other
faint-target, guest-observer science proposals. Weakly illuminated pixels are
dominated by low frequency trends that are both non-astrophysical and
correlated from object to object. A critical clue to understanding this
instrumental noise is that different targets observed in the same channels of
Campaign 8 (rear facing) and Campaign 16 (forward facing) had nearly identical
light curves after time reversal of one of the campaigns. This observation
strongly suggests that the underlying problem relates to the relative
Sun-spacecraft-field orientation, which was approximately the same on day 1 of
Campaign 8 as the last day of Campaign 16. Furthermore, we measure that the
instrumental signature lags in time as a function of radius from the center of
the detector, crossing channel boundaries. Systematics documented in this
investigation are unlikely to be due to Moir\'{e} noise, rolling band, or
pointing jitter. Instead this work strongly suggests temperature-dependent
focus changes that are further subject to channel variations. Further
characterization of this signature is crucial for rehabilitating K2 data for
use in investigations of AGN light curves.
