We report the discovery of an occultation event in the low-luminosity narrow-line Seyfert 1 galaxy WPVS 007 in 2015 February and March. In concert with longer timescale variability, these observations place strong constraints on the nature and location of the absorbing material. Swift monitoring has revealed a secular decrease since ~2010 accompanied by flattening of the optical and UV photometry that suggests variable reddening. Analysis of four Hubble Space Telescope COS observations since 2010, including a Directors Discretionary time observation during the occultation, shows that the broad-absorption-line velocity offset and the CIV emission-line width both decrease as the reddening increases. The occultation dynamical timescale, the BAL variability dynamical timescale, and the density of the BAL gas show that both the reddening material and the broad-absorption-line gas are consistent with an origin in the torus. These observations can be explained by a scenario in which the torus is clumpy with variable scale height, and the BAL gas is blown from the torus material like spray from the crest of a wave. As the obscuring material passes into our line of sight, we alternately see high-velocity broad absorption lines and a clear view to the central engine, or low-velocity broad absorption lines and strong reddening. WPVS 007 has a small black hole mass, and correspondingly short timescales, and so we may be observing behavior that is common in BALQSOs, but is not typically observable.