You can breed them while they are mounted on the wall. I found it's the best way to breed them because they don't move around. But be carefully their egg goes to the other side of the wall so make sure you have access to both sides.
I love these guys. Don't think of them as standard battle mounts. I use mine to have a really fun time tracking and hunting down creatures in the Ragnarok canyon. Because you can shoot from it's saddle, you can wait to ambush potentially dangerous creatures from the walls and bridges. By far my favorite hunting mount.
Once tamed they are actually okay at swimming and excellent guard animals for if you're base gets raided just put them on the ceiling and when someone breaks in it drops on them and gives them rabies which will generally kill them quickly
These things can stay hooked to any surface even when unmounted. If you live in a cave or wanna set an ambush leave them hooked to the cave entrance ceiling on agressive and taunt your enemies to follow you into the cave.
They'll shit their pants trust me...