https://www.bg-wiki.com/ffxi/Curio_Vendor_Moogle#Various_Key_Items
bg-wiki.com said:
*Players must be in possession of the previous rank's wildcat badge and have met the prerequisites for undertaking the appropriate promotion quest in order to purchase these items. You will only be offered the rank available to you. You will immediately receive your new rank and the appropriate title. You do not need to start the "Promotion" quest in order do have the option to buy them.
If you have done the test/quest to rank up on your main, no shame in getting around doing it again on your alt since you can just buy the key item to skip the ordeal.
Edit: Oh, nevermind. There isn't one for the Captain rank. Still, if you're in the middle of getting there, this may be helpful still so I won't delete the post.