  We present near-infrared $JHK_s$ photometry and light curves of the candidate
magnetic white dwarf+brown dwarf binary SDSS J121209.31+013627.7 and report on
the detection of near-infrared excess and variability in the $K_s-$band. The
observed near-infrared excess can be explained by the presence of an L7 brown
dwarf and an extra emission source. The $J$ and $H$ light curves appear flat,
which rules out eclipses deeper than 0.2 mag and the presence of an accretion
hot spot on the white dwarf. From the variable $K_s$ lightcurve, we get a
refined period for the system of 88$\pm$1 minutes. We show that the observed
variability in $K_s-$band can be explained by cyclotron emission, which can be
modeled by a small spot on the surface of the white dwarf. SDSS 1212 exhibits
similarities to the ultra-short period polar EF Eridani, however the lack of
evidence for Roche-lobe overflow accretion suggests it may be a pre-polar.
