There is usually at least one quetz roaming around craggs Island and the red obelisk. This method works especially well on evolution event. Go to red obelisk, kill any and all quetzals there that are not of your liking, then fly to above the nearby swamp (or further). Then fly back and check above the small beach part between the obelisk and craggs which is separated to craggs by a thin water path. If no quetzal is there then check around and west of the obelisk. This works 85% of the time for me on evolution event. If no quetz did spawn then try flying further or waiting 10 sec before going back.
The fun way is to jump off and grapple to your argie and whistle it to attack and since argies are slow it won’t catch up in time so tranq till it goes out also bring parachutes and consider liking so more people will know
If you drop a quetzal due to knockout, and it lands next to a giga...just know, the quetzal belong to the giga. Now you get to watch your would be quetzal get eaten by a giga. Now you can go home and cry.