\[eq:pixelphase\]) is very strongly favored for each observation. This is likely because the pixel phase effect has a much larger effect on the photometry than the low-amplitude astrophysical variability. Since the results of the simultaneous fit are more highly correlated with pixel position than the original fit, we use the light curves obtained using the the cubic correction model (Equation \[eq:pixelphase\]) for the rest of the analysis.]{}

Assessing the evidence for phase shifts between channels
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We investigate the possibility of phase shifts between the $3.6~\mu$m and $4.5~\mu$m light curves. Different wavelengths probe different pressure levels in brown dwarf atmospheres [@Buenzli2012], and phase shifts can potentially provide valuable information on the vertical atmospheric structure. Phase shifts have been observed in a number of brown dwarfs over the $1-5~\mu$m wavelength range [@Buenzli2012; @Yang2016; @Biller2018], but have not been reported between *Spitzer* Channels 1 and 2 [@Metchev2015a; @Yang2016]. Since the $3.6~\mu$m and $4.5~\mu$m bands probe similar atmospheric pressures [@Yang2016], phase shifts are not generally expected at these wavelengths. [The BIC framework described in Section \[sec:BIC\] also provides a robust method to determine whether the data warrant the addition of a phase shift between the $3.6~\mu$m and $4.5~\mu$m light curves for and . 