This study examines the exciton dynamics in InGaN/GaN core-shell nanorods using time-resolved cathodoluminescence (TRCL), which provides nanometer-scale lateral spatial and tens of picoseconds temporal resolutions. The focus is on thick (>20 nm) InGaN layers on the non-polar, semi-polar and polar InGaN facets, which are accessible for study due to the unique nanorod geometry. Spectrally integrated TRCL decay transients reveal distinct recombination behaviours across these facets, indicating varied exciton lifetimes. By extracting fast and slow lifetime components and observing their temperature trends along with those of the integrated and peak intensity, the differences in behaviour were linked to variations in point defect density and the degree and density of localisation centres in the different regions. Further analysis shows that the non-polar and polar regions demonstrate increasing lifetimes with decreasing emission energy, attributed to an increase in the depth of localisation. The semi-polar facet instead showed a spectral independence of the lifetime which could not be rationalised by an absence of exciton localisation. This investigation provides insights into the intricate exciton dynamics in InGaN/GaN nanorods, offering valuable information for the design and development of optoelectronic devices.