That''s not really a "dark system", that's a "test system". There are at least three "secret" star systems within 1 LY of Sol; they are invisible on the galaxy map but still visible on the skybox from neighbouring systems; one of them is a red giant star, so it's actually visible from quite far away. One of these systems is named "Singlelighttest", which gives some idea of the purpose of these systems: as a playground for FD to test stuff during the live game, far away from prying eyes. They can also use these systems as dumping grounds for "deleted" factions such as Emperor's Dawn, since apparently there can be no such thing as a "deleted faction" or a "homeless faction".
For some further discussion and pictures of these "test systems", check out
this old thread. Doing a forum search for "Singlelighttest" also dregs up all sorts of discussion from the early days of the game, including that the co-ordinates of Singlelighttest are (-0.25, 0.25, 0.25); the co-ords of Wregoe YK-P e5-83 appear to be (-0.5, 0, 0.5), so it's not another name for the same star system. Several other Test systems were also spotted and reported back in those early days: Test, Test2, Test3, and TestRender. I don't know if all of these test systems are all very close to Sol. "Singlelighttest" attracted more attention in the forums because it is inhabited, with a commodity market, and for quite a long time after game launch was still listed in the commodity source/destination lists in the commodity markets around Sol.
Having the Sol permit won't help you get there, since, as already noted, it is forbidden to travel from one star system to another in Supercruise. It's a "Sol permit", not a "Wregoe YK-P e5-83 permit".