And in 1.20b we'll have...

[Altano]

So with multiple mounts available, how do we choose which one to call?

I would suggest they just make the "chocobo" button in the micro menu become a "call mount" button for those who have unlocked a 2nd mount, which would then trigger a small popup window of "Which mount will you call?", much like the popup for choosing which retainer to summon.