  High precision lightcurves combined with eclipse mapping techniques can
reveal the horizontal and vertical structure of a planet's thermal emission and
the dynamics of hot Jupiters. Someday, they even may reveal the surface maps of
rocky planets. However, inverting lightcurves into maps requires an
understanding of the planet, star and instrumental trends because they can
resemble the gradual flux variations as the planet rotates (ie. partial phase
curves). In this work, we simulate lightcurves with baseline trends and assess
the impact on planet maps. Baseline trends can be erroneously modeled by
incorrect astrophysical planet map features, but there are clues to avoid this
pitfall in both the residuals of the lightcurve during eclipse and sharp
features at the terminator of the planet. Models that use a Gaussian process or
polynomial to account for a baseline trend successfully recover the input map
even in the presence of systematics but with worse precision for the m=1
spherical harmonic terms. This is also confirmed with the ThERESA eigencurve
method where fewer lightcurve terms can model the planet without correlations
between the components. These conclusions help aid the decision on how to
schedule observations to improve map precision. If the m=1 components are
critical, such as measuring the East/West hotspot shift on a hot Jupiter,
better characterization of baseline trends can improve the m=1 terms'
precision. For latitudinal North/South information from the remaining mapping
terms, it is preferable to obtain high signal-to-noise at ingress/egress with
more eclipses.
