Light emission from the gap of a scanning tunneling microscope can be used to investigate many optoelectronic processes at the single-molecule level and to gain insight into the fundamental photophysical mechanisms involved. One important issue is how to improve the quantum efficiency of quantum emitters in the nanometer-sized metallic gap so that molecule-specific emission can be clearly observed. Here, using electromagnetic simulations, we systematically investigate the influence of an atomic-scale protrusion at the tip apex on the emission properties of a point dipole in the plasmonic nanocavity. We found that such an atomistic protrusion can induce strong and spatially highly confined electric fields, thus increasing the quantum efficiency of molecular fluorescence over two orders of magnitude even when its dipole is oriented parallel to the metal surface, a situation occurring in most realistic single-molecule electroluminescence experiments. In addition, our theoretical simulations indicate that due to the lightning rod effect induced by the protrusion in a plasmonic nanocavity, the quantum efficiency increases monotonically as the tip approaches the dipole to the point of contact, instead of being quenched, thus explaining previous experimental observations with ever-enhancing fluorescence. Furthermore, we also examine in detail how the protrusion radius, height, and material affect the protrusion-induced emission enhancement. These results are believed to be instructive for further studies on the optoelectronic properties of single molecules in tip-based plasmonic nanocavities.