Common to molecular electronics studies, nanoscale break junctions created through electromigration also naturally produce electroluminescent arrays of individual gold nanoclusters spanning the electrodes. Due to inelastic electron tunneling into cluster electronic energy levels, these several-atom nanoclusters (Au~18-22) exhibit bright, field-dependent, antibunched emission in the near infrared (650800 nm), acting as room-temperature electrically driven single-photon sources. AC electrical excitation with time-stamping of photon arrival times enables fast and local tracking of electrode-nanocluster coupling dynamics demonstrating that charge injection to the clusters is directly modulated by dynamic coupling to individual electrodes. The electrode-nanocluster coupling rate fluctuates by nearly an order of magnitude and, due to the asymmetry of the electromigration process, exhibits preferential charge injection from the anode. Directly reporting on (and often facilitating) nanoscale charge transport, time-tagged single-molecule electroluminescence reveals a significant mechanism for nanoscale charge transport in nanoscale gold break junctions, and offers direct readout of the electrode-molecule interactions that can be correlated with current flow. Single-molecule electroluminescence techniques for characterization of electrode heterogeneity and dynamics as well as implications for future research are discussed.