Theory: the 'spell of starlight' is a scrying or remote-viewing effect which Quirrelmort originally developed to keep an eye on the Pioneer horcrux. It's strenuous because of the extreme range, possible at all only because of the strong sympathetic connection involved. Reinforcing the sympathetic connection is important to maintain the possibility of Apparating out there, and sharing the experience helps to establish a sympathetic link between Harry's scar/mysterious dark side and the horcrux, which will eventually make it possible to do something nasty to him from far away.