We previously obtained constraints on the viewing geometries of 6 Fermi LAT pulsars using a multiwavelength approach (Seyffert et al., 2011). To obtain these constraints we compared the observed radio and $gamma$-ray light curves (LCs) for those 6 pulsars by eye to LCs predicted by geometric models detailing the location and extent of emission regions in a pulsar magnetosphere. As a precursor to obtaining these constraints, a parameter study was conducted to reinforce our qualitative understanding of how the underlying model parameters effect the LCs produced by the geometric models. Extracting useful trends from the $gamma$-ray model LCs proved difficult though due to the increased complexity of the geometric models for the $gamma$-ray emission relative to those for the radio emission. In this paper we explore a second approach to investigating the interplay between the model parameters and the LC atlas. This approach does not attempt to understand how the set of model parameters influences the LC shapes directly, but rather, more fundamentally, investigates how the set of model parameters effects the sky maps from which the latter are extracted. This allows us to also recognise structure within the atlas itself, as we are now able to attribute certain features of the LCs to specific features on the sky map, meaning that we not only understand how the structure of single LCs come about, but also how their structure changes as we move through the geometric solution space.