Convectively unstable disturbances are often described in terms of propagating wave packets that grow and broaden. We extend such a description here and show how it recovers previous results and agrees with simulations. Applying these ideas to the magnetospheric flanks, we find that such wave packets will often not provide a driver of long enough duration for establishing a fully formed field line resonance (FLR). This suggest that the alternative description of the convective instability as a steady wave train radiated by a fixed source may be more appropriate for the flanks on some occasions. Whether the unstable waveguide modes prefer to exist as steady wave trains or convecting wave packets can have important implications for identifying the mechanisms through which the magnetosheath is coupled to the magnetosphere.