Gaudiness is the quality of being gaudy: that too-bright, too-decorated look that feels cheap. You use it when you want to name the flash itself — the gold paint, the fake jewels, the clashing colours — rather than point at one object. It is a slightly formal, written kind of noun; in speech people more often just say something looks gaudy. Like the adjective, it carries disapproval. Brightness and celebration are fine; gaudiness is brightness that has gone loud and tasteless.