Nope: this adjective has absolutely nothing to do with Barry Gibb, though it may be associated with a “night fever” of another kind, since the term is often used to describe the moon. A “gibbous moon” is what you call it when the lunar disc is more than halfway illuminated, but not yet full. It is the “pregnant moon” — the one that frustrates werewolves and geeky lunar eclipse aficionados everywhere.
“Gibbous” also more generally describes an oddly convex shape, a lumpy bulge…anything grotesquely tumescent or otherwise odd-shaped and resembling the head of Stewie Griffin from Family Guy. Gibbous comes from the Latin word “gibbus” which literally means “hump” and the term has been employed to malign hunchbacks by foppish aesthetes everywhere since the 18th century. I hereby propose we deem Wednesday of the work week “Gibbous Day” (instead of the colloquial “Hump Day,” which always sounds nastier than it ever is).
Of course, in “first person shooter” games, any splort of blood or flesh blown off a person’s face is called a “gib”…but this term likely comes from “giblet,” not “gibbous,” as any chicken farmer who has read his HP Lovecraft certainly would know.