Don't bother finding it. It finds you lol. If you even try to find it then you just wasted time if you didn't find it cuz ARK is pretty much weird. If you found a quetz unprepared then request a flying dino(with decent damage or any flying dino if you really want the quetz) then chase the quetz and kill it then get its implant. After getting the implant then get yourself spawn pod(?) Or spawn it at an obelisk BUT REMEMBER! MAKE A TAMING PEN AROUND THE OBELISK OR WHERE YOU'RE MAKING THE SPAWN POD(?). also while you're doing this, get some amber(for mobile)! Trust me you have alot of time getting amber since the implant expires for about 2.5 days(?)
I Was on a Tapejara and somehow knocked one when I was on lvl57 and that fool quetzal fell and landed in front of a group of allosaurs. That was the first and last quetzal I found in my game😭.... Now search continues but no luck..... #RIPMe
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!