We report the results of a 10-yr photometric program on BG Canis Minoris, a nova-like variable distinguished by the presence of a strictly coherent 913-s wave in its light curve. We present long-term ephemerides for the orbital clock, which manifests itself through a 3.2-h light modulation, and the 913-s clock. The former is found to be quite stable, and may originate from partial obscuration of the white dwarf by a bloated bright spot at the outer edge of the disk. The rapid oscillation shows a period decreasing on a time scale of 4 X 10(5) yr, consistent with the idea that a magnetic white dwarf is spinning up under the torques exerted by accreting gas. The P measurement requires M > 7 X 10(-10) M. yr-1; combining the constraints from P and the polarization, we estimate a magnetospheric radius about equal to the corotation radius, with M almost-equal-to 10(-9) M. yr-1. Power spectra of the light curves reveal evidence for other high-frequency signals which seem to be related to the 913-s pulse. Features that may be stable in period, though not in amplitude, are found at 1073 +/- 8 and 1977 +/- 10 s. The former probably arises from reprocessing of the pulsed light in structures which are in prograde orbit around the white dwarf-f. We find no particularly simple way to understand the other peak, but there is a substantial hint that the true rotation period of the white dwarf is 1827 s, not 913 s.