I know this has been reported before but the Yellow Cactus Hopper is still not showing in the pet tab.
I've noticed it will appear if you pass through a transition area (Doors to shops or Area to Area) unless you have mount equipped. It seems as though with Cactus Hopper the character remains in Mount Mode and your pet won't appear. If you unmounted before passing through a transition area the pet remains invisible until you pass through the area then it will appear.
I have the Pink Cactus Hopper and it’s kind of the same issue. If I’m on a mount, pet equipped, and then dismount, it doesn’t show up beside me or in my spell book. But if I teleport to my dorm (no mount) it shows up. If I load into an area on a mount with the pet equipped and then dismount, it’s invisible. But if I load into an area with no mount and the pet equipped, it shows up.