We introduce a wait-and-chase scheme that models the contact times between moving agents within a connectionist construct. The idea that elementary processors move within a network to get a proper position is borne out both by biological neurons in the brain morphogenesis and by agents within social networks. From the former, we take inspiration to devise a medium-term project for new artificial neural network training procedures where mobile neurons exchange data only when they are close to one another in a proper space (are in contact). From the latter, we accumulate mobility tracks experience. We focus on the preliminary step of characterizing the elapsed time between neuron contacts, which results from a spatial process fitting in the family of random processes with memory, where chasing neurons are stochastically driven by the goal of hitting target neurons. Thus, we add an unprecedented mobility model to the literature in the field, introducing a distribution law of the intercontact times that merges features of both negative exponential and Pareto distribution laws. We give a constructive description and implementation of our model, as well as a short analytical form whose parameters are suitably estimated in terms of confidence intervals from experimental data. Numerical experiments show the model and related inference tools to be sufficiently robust to cope with two main requisites for its exploitation in a neural network: the nonindependence of the observed intercontact times and the feasibility of the model inversion problem to infer suitable mobility parameters.