The aim of the search for extraterrestrial intelligence (SETI) is to find technologically capable life beyond Earth through their technosignatures. On 2019 April 29, the Breakthrough Listen SETI project observed Proxima Centauri with the Parkes ‘Murriyang’ radio telescope. These data contained a narrowband signal with characteristics broadly consistent with a technosignature near 982 MHz (‘blc1’). Here we present a procedure for the analysis of potential technosignatures, in the context of the ubiquity of human-generated radio interference, which we apply to blc1. Using this procedure, we find that blc1 is not an extraterrestrial technosignature, but rather an electronically drifting intermodulation product of local, time-varying interferers aligned with the observing cadence. We find dozens of instances of radio interference with similar morphologies to blc1 at frequencies harmonically related to common clock oscillators. These complex intermodulation products highlight the necessity for detailed follow-up of any signal of interest using a procedure such as the one outlined in this work.