I’ve had most my luck finding them at red obelisk, actually only place I’ve found them,so far I’ve found four of them there,one one time then when I go back after I tame it to look around another has spawn there,and before I tamed one I found two low level ones at the same time.i tamed them using raw meat on a griffin. Using longneck rifle with tranq darts,I had good luck because the Quetzel got knocked out right next to my base.well bye and good luck!
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!