The theory of binary star formation predicts that close binaries (a<100au) will experience periodic pulsed accretion events as streams of material form at the inner edge of a circumbinary disk (CBD), cross a dynamically cleared gap, and feed circumstellar disks or accrete directly onto the stars. The archetype for the pulsed accretion theory is the eccentric, short-period, classical T Tauri binary DQ Tau. Low-cadence (~daily) broadband photometry has shown brightening events near most periastron passages, just as numerical simulations would predict for an eccentric binary. Magnetic reconnection events (flares) during the collision of stellar magnetospheres near periastron could, however, produce the same periodic, broadband behavior when observed at a one-day cadence. To reveal the dominant physical mechanism seen in DQ Tau's low-cadence observations, we have obtained continuous, moderate-cadence, multiband photometry over 10 orbital periods, supplemented with 27 nights of minute-cadence photometry centered on four separate periastron passages. While both accretion and stellar flares are present, the dominant timescale and morphology of brightening events are characteristic of accretion. On average, the mass accretion rate increases by a factor of five near periastron, in good agreement with recent models. Large variability is observed in the morphology and amplitude of accretion events from orbit to orbit. We argue that this is due to the absence of stable circumstellar disks around each star, compounded by inhomogeneities at the inner edge of the CBD and within the accretion streams themselves. Quasiperiodic apastron accretion events are also observed, which are not predicted by binary accretion theory.