The title "Vanishing Age" doesn't make sense, right? Especially when paired with the other groups of the Glittering Crux. Actually, it makes perfect sense because Head's Evil Plan involved going and staying back in time, effectively vanishing age, or making age and time disappear. The Spell My Name with an S version, "Banishing Age" makes sense in the same way.
Related to the above: Due to the mark Head received from Shingo, he never ages. So, what does never growing up do? It vanishes age. Who was the head of Vanishing Age? Head.
The Filament section of the Gittering Crux was pretty useless, and their main goal was to gain back the marks their families lost. So why would Head keep them around? Because they're just like him! He never inherited his mark from his father, and so he could sympathize with them.
Takuto is so shy about sex and respectful towards women because he doesn't want to end up like his philandering father.
Sugata can survive merging with a mecha that left all of its previous pilots in a coma because it sucked out their libido. He also has two maids who wear full on maid outfits. The combination of these facts leads this troper to believe that Sugata is, in fact, a massive pervert with a massive libido.