Which player on the account gets the pet when you cash in a gift card? I know all the players can share in the crowns, but it's the pet that is most important.
When the gift card is redeemed, any character on the account can claim the pet. The next time that account is logged in to, a gift icon will appear like this:
Just click on the gift button and you'll see the option to claim the gift or cancel and claim it later. Every character that you log in with on that account will see the gift redemption option.
Even if you claim the pet on the wrong character, you can still place it in the Shared Bank.