Quetz usually spawn at red obelisk, if you don't see one wait a few minutes for t to spawn. If you are looking for a high level kill the lower level one so it another can respawn

For 'The Center' map the common spawn locations tend to be near any obelisk, as well as around 55,45 or cruising around the entirety of Jungle South. It's worth checking around lava island too.

Low levels seem to spawn neared red obbi on the island. If you're looking for one, head over there

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!