Indeed, there is a consistency in Oda's way of making the rays emanate from the weapon or fist of those who possess Haki. He may not redraw it happening with the same character again, but the first panel of its use remains.
Garp has a panel of him using it when he arrived on the island, which tells us that Garp possesses Haki since it was overflowing from his fist. However, Kuzan does not have such a panel; the only thing the guy has is an ice glove. That's why admirals' fans are desperate, simply because Kuzan has proven to be incapable of harming Kaidou and is being defeated in a mid-difficulty battle.