In this paper, we present a simple strategy to identify Non-Terrestrial artefacts [NTAs; Haqq-Misra and Kopparapu (2012)] in or near geosynchronous Earth orbits (GEOs). We show that even the small pieces of reflective debris in orbit around the Earth can be identified through searches for multiple transients in old photographic plate material exposed before the launch of first human satellite in 1957. In order to separate between possible false point-like sources on photographic plates from real reflections, we present calculations to quantify the associated probabilities of alignments. We show that in an image with nine "simultaneous transients" at least four or five point sources along a line within a 10 * 10 arcmin(2) image box are a strong indicator of NTAs, corresponding to significance levels of 2.5 to 3.9 sigma. This given methodology can then be applied to set an upper limit to the prevalence of NTAs with reflective surfaces in geosynchronous orbits.