  Mapping exoplanets across phases and during secondary eclipse is a powerful
technique for characterizing Hot Jupiters in emission. Since these planets are
expected to rotate about axes normal to their orbital planes, with rotation
periods synchronized with their orbital periods, mapping provides a direct
correspondence between orbital phase and planetary longitude. We develop a
framework to understand the information content of planets where their rotation
states are not well constrained, by constructing bases of light curves across
different rotation rates and obliquities that are orthogonal in integrated flux
across secondary eclipse. These demonstrate that brightness variability during
eclipse may arise from a variety of rotation rates, obliquities, and map
structures, requiring priors to properly disentangle each of these components.
By modeling eclipse observations of the Warm Jupiter HAT-P-18 b we demonstrate
that, at a signal-to-noise equivalent to $\sim 10$ orbits with JWST, confusion
about map structure is likely a concern only at the upper physical limits of
possible rotation rates. Even without priors, one may nevertheless be able to
put an order-of-magnitude constraint on rotation rate by determining at what
rates the fitted map complexity is minimized, a prescription whose efficacy
increases if out-of-eclipse data are available to isolate the effects of
rotation. Finally, in the limit of maps with longitudinal symmetry, the
projected obliquity in the plane of the sky determines the information
available during eclipse, ranging from non-detections of structure to a basic
constraint on hemispherical asymmetry and orientation depending on the
obliquity angle.
