The authors suggest monitoring the changes in brightness with distance for a set of Kuiper Belt Objects (KBOs). Naturally illuminated objects will have a slope of -4, due to the inverse square law affecting both the light incident on the object, and the reflected light traveling to us. However, the slope will be less than -4 (and greater than -2) if the object is artificially illuminated (i.e., producing light on its surface). Therefore, monitoring the changes of brightness with distance for KBOs may be a viable approach to finding Solar System artifacts.
I am skeptical about the efficacy of this approach, as there are a number of natural factors (aside from changing distance from the Sun and us) that may cause an object’s brightness to change, as the authors explicitly mention. Some of the specific factors raised by the authors include a changing phase angle (due to Earth’s orbital motion), rotation of objects with nonuniform shapes or surface albedos, or occultations by nearby objects. Another issue is the extremely long periods of KBOs, so a long temporal baseline is required to measure the slope of the relation. Further, the artificial light must persist for an incredibly long time.
While the practicality of this idea is questionable (perhaps to put it generously) the originality makes it very worthwhile.