I usually see a lot of Quezal’s around the volcano on Ragnarok. For solo taming herd it towards the side of a mountain or just a place where it can get stuck by a lot of rocks (I did the canyon). You can herd it by attacking the Quez once and just let it run away in the direction you want it to, although I’ve heard rare flowers make it follow you but I’ve never tried that. For this I suggest to tame a high level Queztal so it won’t die from your attacks. Mutton is the best after the kibble and you can find ovis’ on the green patch by the scar on Ragnarok (not far from the Queztal spawn) so stock up first. Ovis’ are not directly next to the scar but further into the green land. Good luck!! And if this tip help name your queztal Elvis Pretzel.
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.
To solo tame, grapple to an argentavis, and be ready to set your argentavis to passive and attack my target on command. Just maintain a process of having your argentavis chase the quetzal, when you get close enough set it passive, then fire a tranq dart/arrow. This is a long process, but it is by far the easiest way to solo tame, unless you already have a quetzal.
This tip is only if you already have a quetzal available. The easiest way to tame a quetz, is to build a quetz catcher. You can make it out of thatch and its hands down the best tactic. A lot of YouTube videos available on how to build one. Knock it out in the catcher, and you don't have to worry about it getting hit.