The El NinoSouthern Oscillation (ENSO) is driven by oceanatmosphere interactions in the equatorial Pacific, and this variability is often attributed to coupled modes that are evidenced by the temporal stability analysis of anomaly models. Here, the further diagnostic of absolute/convective instability is considered, which assesses whether small perturbations localized in space and time (e.g. random wind disturbances) lead to instabilities that develop in-place or propagate away from the perturbed region. It is shown that boundary conditions play a secondary role for this approach and that the development of large-scale wave packets in the equatorial Pacific basin is possible, as in the case of an infinite domain. As an illustration, two simple coupled models are diagnosed that rely either on thermocline processes or zonal advective processes. The model with thermocline processes is absolutely unstable' and therefore develops intrinsic oscillations, while the model with zonal advective processes is convectively unstable' and therefore acts as a noise amplifier. The identification of the two instability regimes may characterize different ENSO formation mechanisms as a response to random wind disturbances. For the absolutely unstable regime, a standing ENSO-like oscillation can develop in the equatorial Pacific without involving boundary reflections, while for the convectively unstable regime boundary reflections are essential.