Thank to the pursuit:"tame a Quetzal"(mobile) i have managed to uncover alot of Quetzal spawn locations on the island map

-one at the red obelisk

-one at the curve looking island south of the red obelisk

-one directly at the blue obelisk

-one near east of the snow mountain(the one that have no obelisk)

-one at the waterfall west of the volcano

-one near a waterfall to the south-west of the volcano

-one to the south next to the mountain east of the volcano

-one next to the mountain north-east of the volcano(not the snow one)

-one at the part where small river fuse into one, east of the volcano(not the one near red wood)

-one at the green obelisk

-one near north of the obelisk

I did managed to find couple of quetzal spawning at some of those location and killed them (cuz they low level)

Everytime a quetzal spawn it alway spawn a little above the ground and fly away so be sure to search below first

Anyway happy hunting

Also for those mobiler wondering, you need to be lv 77 and had already completed pursuit "tame a bronto" to unlock this pursuit