Positive ion desorption following electron impact dissociative ionization of ethane adsorbed on Ar, Kr, and Xe multilayers has been studied as a function of incident electron energy from threshold to 100 eV. Based on the dependence of ion yields on the identity of the rare gas, it is likely that the majority of ethane molecules undergo indirect ionization following hole transfer from the ionized underlying rare gas. This has also been corroborated by density of states calculations showing the energetic alignment of the outer valence states of ethane and the condensed rare gas ionization energies. Due to the near-resonant nature of charge transfer for single-hole states, the ethane molecular ion is excited to different final ionic states on different rare gases, which leads to differences in ion desorption yields and branching ratios. The quantitative yields increase with increasing ionization energy gap between the rare gas and ethane, in the order Ar > Kr > Xe. The large increase in yields from 25 eV onwards for all rare gases is likely due to the formation and decay of two-hole states on neighboring rare gas and ethane molecules due to interatomic and intermolecular Coulomb decay (ICD) and not electron transfer mediated decay (ETMD). The ICD and ETMD pathways become accessible when the incoming electron has sufficient energy to excite the inner valence ns level of the rare gas to a Rydberg state or ionize it. The experimental findings are supported by calculations of thresholds, density of states for the final configurations of these processes, and coupling strengths for hole transfer between ethane and rare gases. The fragment ion branching ratios vary with energy from threshold to about 35 eV, showing the fragmentation pattern changes with the mode of hole transfer and availability of excess energy. Sigma C-C bonds are more likely to break than C-H bonds in the mid-20 eV range, and this effect is most pronounced for Xe, followed by Kr, and then Ar.