High spatial and energy resolution EELS can be employed for detailed characterization of both localized and propagating surface plasmon excitations supported by metal nanostructures, giving insight into fundamental physical phenomena involved in various plasmonic effects. Here, applying EELS to ultra-sharp convex grooves in gold, we directly probe extremely confined gap surface plasmon (GSP) modes excited by swift electrons in nanometer-wide gaps. Both experimental and theoretical EELS data reveal the resonance behavior associated with the excitation of the antisymmetric (with respect to the transverse electric-field component) GSP mode for extremely small gap widths, down to ~5 nm. It is argued that the excitation of this mode, featuring very strong absorption, plays a crucial role in the experimental realization of non-resonant light absorption by ultra-sharp convex grooves with fabrication-induced asymmetry. Occurrence of the antisymmetric GSP mode along with the fundamental GSP mode exploited in plasmonic waveguides with extreme light confinement is a very important factor that should be taken into account in the design of plasmonic nanophotonic circuits and devices. ; Comment: 7 pages, including 4 figures. Supplemental Material is available upon request to authors