($\%$)   Period (hr)              Phase (rad)           $\Delta$BIC
  \[0.5ex\]     L2$\gamma$   1         $0.18\pm0.04$      $2.37^{+0.08}_{-0.06}$   $1.2^{+0.9}_{-0.7}$   $-44$
                             2         $0.16\pm0.04$      $2.43^{+0.09}_{-0.10}$   $2.7\pm0.3$           $-28$
                L3$\gamma$   1         $0.36\pm0.04$      $18.5^{+0.8}_{-0.7}$     $5.0\pm0.4$           $-212$
                             2         $0.24\pm0.04$      $14.7^{+0.9}_{-0.8}$     $2.6\pm0.3$           $-69$
                             1&2       $0.28\pm0.02$      $15.7\pm0.2$             $3.1\pm0.1$           
                L4$\gamma$   1         $<0.16$            $<5.6$                   ...                   $17$
                             2         $<0.18$            $<5.6$                   ...                   $17$
  \[0.5ex\]                                                                                              
  ------------- ------------ --------- ------------------ ------------------------ --------------------- -------------

We show the final posterior distributions of the variability amplitude, rotation period and phase in Figures \[fig:posterior\_2M0045\] and \[fig:posterior\_2M0501\], and present the best-fit parameters and their 1-$\sigma$ errors in Table \[tab:parameters\]. We overplot the best-fit sinusoidal model for each channel in Figures \[fig:2M0045\_full\_lc\] and \[fig:2M0501\_full\_lc\]. The residuals of the fit are normally distributed. For , the measured rotation periods of $2.37^{+0.08}_{-0.06}$ hr at $3.6~\mu$m and $2.43^{+0.09}_{-0.10}$ hr at $4.5~\mu$m are fully consistent. In contrast, the two rotation periods obtained for are quite different – $18.5^{+0.8}_{-0.7}$ hr at $3.6~\mu$m and $14.7^{+0.9}_{-.8}$ hr at $4.5~\mu$m. While the longer period fits the $3.6~\mu$m well, it does not provide a good fit to the $4.5~\mu$m data. The shorter period does a better job of fitting both channels. To estimate the most accurate rotation period for we fit a sinusoidal model to both channels simultaneously, finding a period of $15.7\pm0.2~$hr. [We show the 