Optical spectromicroscopies, which can reach atomic resolution due to plasmonic enhancement, are perturbed by spontaneous intensity modifications. Here, we study such fluctuations in plasmonic electroluminescence at the single-atom limit profiting from the precision of a low-temperature scanning tunneling microscope. First, we investigate the influence of a controlled single-atom transfer from the tip to the sample on the plasmonic properties of the junction. Next, we form a well-defined atomic contact of several quanta of conductance. In contact, we observe changes of the electroluminescence intensity that can be assigned to spontaneous modifications of electronic conductance, plasmonic excitation, and optical antenna properties all originating from minute atomic rearrangements at or near the contact. Our observations are relevant for the understanding of processes leading to spontaneous intensity variations in plasmon-enhanced atomic-scale spectroscopies such as intensity blinking in picocavities.