Now over seven years into its journey beyond the heliopause, Voyager 1 continues to return unprecedented observations of energetic particles, magnetic fields, and plasma emissions from the very local interstellar medium. Shortly after its heliopause crossing, Voyager 1 discovered an unusual time-varying galactic cosmic-ray anisotropy, characterized by smoothly changing intensity reductions in particles propagating nearly perpendicular to the magnetic field; outside of this isolated region, cosmic rays appear mostly unvarying, without a significant radial gradient. These small (~15%) but lasting (~100 to ~630 days) anisotropic events are still not fully understood. Nevertheless, they serve as clear markers, together with shorter-lived cosmic-ray intensity enhancements, electron plasma oscillations, and weak laminar shocks, that even beyond the heliopause, the Sun's variable output significantly influences its surroundings. So far, these unusual energetic particle occurrences have mainly been studied using integrated proton intensities of ~20 MeV and higher. Using data from the Voyager 1 Cosmic Ray Subsystem, we extend the analysis to electrons, as well as lower energy protons, and discover the surprising new result that the ~3 to ~105 MeV electrons remain mostly isotropic and unchanging, in sharp contrast to their proton counterparts. We search for clues to explain this underlying species dependence and rule out potential causes related to instrumental effects, velocity and energy, trapping and energy loss, drifts, and turbulence-induced scattering. We also explore some plausible mechanisms and open the door for more detailed follow-up theories and simulations.