Yeah, you can just run FFXIV twice to multibox on 2 characters.

If multiple service accounts are in the same square enix account, you will always see a box to select which one you want to use every time you select a datacenter, whether or not you are multiboxing.

You can definitely play on 2 instances using a single Square Enix account with 2 FFXIV service accounts. First, launch FFXIV, choose your datacenter, then it will ask which service account you want to use. Pick a service account, then login with your character is usual. Then open up the second window. Choose a datacenter, select your second service account, and pick a character. You now have both accounts logged in. After both instances of FFXIV are logged in to their respective service accounts, you can freely change characters within the same datacenter by logging out and then just clicking start. Each FFXIV window will remember which service account it was logged in to.

Make sure to avoid logging in to the same service account on the two instances. Doing so will invalidate the login credentials for the first instance. You will then have to close that instance and open ffxiv again.