There is usually at least one quetz roaming around the red obelisk and craggs Island. Go over there and kill any and all quetzals that aren't of your liking, and then fly to above the nearby swamp or The end of the red lake (or further). Then fly back and be sure to check above the beach area between craggs and the obelisk which is separated to craggs by a thin water path. If no quetzal has spawned there then look around and west of the obelisk. If no quetzal has been found in either area then try flying further away or waiting 10 sec before going back. This method works especially well on evolution event which is when I've mostly tried it. Good luck!
They aren’t always near obelisks. I have been searching for one for days now, have circled the island many times and even done a server reset and have yet to see one near an obelisk. The 2 I did find were near the redwoods and died upon KO due to a troodon pack
Sometimes their at mountains (bases or peaks) other times you can find one above or near the redwoods or a forest, me and my friend found one above the swamp also, and tranqed it out finally in the redwoods, if it fell a little lower it would have drowned.