Recent experimental evidence suggests that the capillary heterogeneity associated with fracture intersections can act to impose temporal and spatial structure on network-scale flows. A simple intersection between orthogonal fractures, one horizontal and the other vertical, has been shown to integrate unsaturated flows. At low flows the intersection forms a capillary barrier that accumulates water in a growing pool. Eventually, the retaining meniscus snaps, discharging a pulse of water. Here we develop a mechanistic explanation for this observed behavior and experimentally consider three perturbations to the geometry of the simple orthogonal intersection. Two of the perturbations also act as capillary barriers, while the third formed a capillary bridge across the intersection. At low flow, all of our experimental intersections imposed a temporal signal, with the nature of that signal dependent on intersection geometry and participation by the horizontal fractures in dynamic storage. At high flow a continuous fluid tendril spanned the system from inlet to outlet with water pooled above the intersection caused by a narrow fluid connection that restricted flow across the intersection. Results from all experiments suggest that pulsation is critically sensitive to small variations in the geometry of fracture intersections and storage in the horizontal fractures. When combined with dependency on supply rate, this sensitivity can generate pulsation of flow across a wide range of time periods and discharge volumes.