The San Andreas fault is one of the most extensively studied faults in the world, yet its physical character and deformation mode beneath the relatively shallow earthquake-generating portion remain largely unconstrained. Tectonic 'non-volcanic' tremor, a recently discovered seismic signal probably generated by shear slip on the deep extension of some major faults, can provide new insight into the deep fate of such faults, including that of the San Andreas fault near Parkfield, California. Here I examine continuous seismic data from mid-2001 to 2008, identifying tremor and decomposing the signal into different families of activity based on the shape and timing of the waveforms at multiple stations. This approach allows differentiation between activities from nearby patches of the deep fault and begins to unveil rich and complex patterns of tremor occurrence. I find that tremor exhibits nearly continuous migration, with the most extensive episodes propagating more than 20 kilometres along fault strike at rates of 15-80 kilometres per hour. This suggests that the San Andreas fault remains a localized through-going structure, at least to the base of the crust, in this area. Tremor rates and recurrence behaviour changed markedly in the wake of the 2004 magnitude-6.0 Parkfield earthquake, but these changes were far from uniform within the tremor zone, probably reflecting heterogeneous fault properties and static and dynamic stresses decaying away from the rupture. The systematic recurrence of tremor demonstrated here suggests the potential to monitor detailed time-varying deformation on this portion of the deep San Andreas fault, deformation which unsteadily loads the shallower zone that last ruptured in the 1857 magnitude-7.9 Fort Tejon earthquake.