System config > keybinds> hotbars.

Then just scroll down to whichever hotbar you want and set a bind...

If your using a gaming mouse you may need to use the mouse software to rebind the buttons. As I'm not sure the game recognises mouse12 for example. But you can set that button to mimic a key combo and bind that to your mount in game.

I set some of my mouse buttons to be ctrl+shift+z x c v b n m in the mouse software

And then just put those binds to hotbar 10 in the ffxiv keybind settings.

Did the same thing with my xbox elite controller paddles. So then paddles on the back trigger the first 4 actions on hotbar 10 as they're mapped to those keybinds.