Once it is up, it may walk along a path, or it may sit for a while. The daily quest is called Once you’ve got your greens in hand it’s time to go Alpaca hunting! This Alpaca loves to get around there are at least 15 possible spawn locations for it — so finding it can be a bit daunting.

You then need to feed it some Seaside Leafy Greens Mix, which can be purchased from many Battle for Azeroth vendors, so pre-purchase some and have them in your bags, ready! Luckily the Elusive Alpaca is just looking for a snack so you only need to bring one along. It won't be up for long: after a few minutes, it will kick people away and despawn. This is the Elusive Quickhoof alpaca. These NPCs spawn every 10 minutes and offer a daily quest for a player. The way to get the mount is by completing this daily quest for 7 times and get the mount reward. This mount also requires feeding but the pattern is different: a single Elusive Quickhoof alpaca will spawn in Vol'dun.

Friendly Alpaca has numerous spawn points around Uldum. Combined waypoints for spawn points mentioned in several comments: /way Vol'dun 26.4 52.5 Alpaca 1 /way Vol'dun 28.0 65.0 Alpaca 2 /way Vol'dun 31.1 67.3 Alpaca 3 /way Vol'dun 42.0 60.0 Alpaca 4 /way Vol'dun 43.0 69.0 Alpaca 5 /way Vol'dun 51.1 85.9 Alpaca 6 /way Vol'dun 52.5 89.0 Alpaca 7 /way Vol'dun 54.0 83.0 Alpaca 8 /way Vol'dun 54.6 53.2 Alpaca 9 /way Vol'dun 55.0 73.0 Alpaca 10. It has a number of spawn points, and a long re-spawn timer of up to 6 hours. * Edit: Today I saw the Alpaca spawn at 70:39 and after it despawned while I was still in the area respawned 5 min later at 76:68 so may not have the long respawn timer previously reported. In the zone of Uldum, there are a couple of friendly NPC spawns by the name of Friendly Alpaca.

To obtain this mount you must be lucky and come across the rare spawn Elusive Quickhoof that wanders Vol'dun.
Combined waypoints for spawn points mentioned in comments here: /way Vol'dun 26.4 52.5 Alpaca 1 /way Vol'dun 28.0 65.0 Alpaca 2 /way Vol'dun 31.1 67.3 Alpaca 3 /way Vol'dun 42.0 60.0 Alpaca 4 /way Vol'dun 43.0 69.0 Alpaca 5 /way Vol'dun 51.1 85.9 Alpaca 6 /way Vol'dun 52.5 89.0 Alpaca 7 /way Vol'dun 54.0 83.0 Alpaca 8 /way Vol'dun 54.6 53.2 Alpaca 9 /way Vol'dun 55.0 73.0 Alpaca 10. He will show up for around 10 minutes before despawning and seems to have a long respawn timer. This Alpaca mount is the easiest to get out of all three alpaca mounts.