Since the observation of single-molecule surface-enhanced Raman scattering (SMSERS) in 1997, questions regarding the nature of the electromagnetic hot spots responsible for such observations still persist. For the first time, we employ electron-energy-loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) to obtain maps of the localized surface plasmon modes of SMSERS-active nanostructures, which are resolved in both space and energy. Single-molecule character is confirmed by the bianalyte approach using two isotopologues of Rhodamine 6G. Surprisingly, the STEM/EELS plasmon maps do not show any direct signature of an electromagnetic hot spot in the gaps between the nanoparticles. The origins of this observation are explored using a fully three-dimensional electrodynamics simulation of both the electron-energy-loss probability and the near-electric field enhancements. The calculations suggest that electron beam excitation of the hot spot is possible, but only when the electron beam is located outside of the junction region.