To understand how neurons and nervous systems first evolved, we need an account of the origins of neural elongations: why did neural elongations (axons and dendrites) first originate, such that they could become the central component of both neurons and nervous systems? Two contrasting conceptual accounts provide different answers to this question. Braitenberg's vehicles provide the iconic illustration of the dominant input-output (IO) view. Here, the basic role of neural elongations is to connect sensors to effectors, both situated at different positions within the body. For this function, neural elongations are thought of as comparatively long and specific connections, which require an articulated body involving substantial developmental processes to build. Internal coordination (IC) models stress a different function for early nervous systems. Here, the coordination of activity across extended parts of a multicellular body is held central, in particular, for the contractions of (muscle) tissue. An IC perspective allows the hypothesis that the earliest proto-neural elongations could have been functional even when they were initially simple, short and random connections, as long as they enhanced the patterning of contractile activity across a multicellular surface. The present computational study provides a proof of concept that such short and random neural elongations can play this role. While an excitable epithelium can generate basic forms of patterning for small body configurations, adding elongations allows such patterning to scale up to larger bodies. This result supports a new, more gradual evolutionary route towards the origins of the very first neurons and nervous systems.