I don't know how much of a permanent solution this is, I just figured this out on my own, I had the same problem as you, I am also relatively new. What I did to get them to hover in place (a.k.a. flap their wings in the air) was making them flyable with ".npc set flyable", using ".npc move" to move them to where I wanted them in the air and then using the command ".npc set autohover always" (I don't know if the always matters instead of dynamic, etc., but I did that for my personal use).
After putting the auto hover on, I removed their flyability by repeating the command ".npc set flyable", and then did it again to give them flying back, so once more: ".npc set flyable", should say in the chat they can fly, and the mount's wings should start moving.
It worked for me, I hope it works for you too! ❤️
