Electrically connected and plasmonically enhanced molecular junctions combine the optical functionalities of high field confinement and enhancement (cavity function), and of high radiative efficiency (antenna function) with the electrical functionalities of molecular transport. Such combined optical and electrical probes have proven useful for the fundamental understanding of metal-molecule contacts and contribute to the development of nanoscale optoelectronic devices including ultrafast electronics and nanosensors. Here, we employ a self-assembled metal-molecule-metal junction with a nanoparticle bridge to investigate correlated fluctuations in conductance and tunneling-induced light emission at room temperature. Despite the presence of hundreds of molecules in the junction, the electrical conductance and light emission are both highly sensitive to atomic-scale fluctuations-a phenomenology reminiscent of picocavities observed in Raman scattering and of luminescence blinking from photoexcited plasmonic junctions. Discrete steps in conductance associated with fluctuating emission intensities through the multiple plasmonic modes of the junction are consistent with a finite number of randomly localized, point-like sources dominating the optoelectronic response. Contrasting with these microscopic fluctuations, the overall plasmonic and electronic functionalities of our devices feature long-term survival at room temperature and under an electrical bias of a few volts, allowing for measurements over several months.