An easier way to trap and tame a Quetzal is to kill it, take its implant, build a big cage around an Obelisk, and revive it. You can then spam tranq arrows at it and tame your beloved Quetzal. Good Luck, Mate! ~WildRapter
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.
If you manage to knock a quetzal out, try starve taming. If you never tried starve taming it’s just leaving a Dino’s hunger go to half way or lower and then you start feeding. I’ve done this many times and it’s very useful taming trick.