While it is possible to run games from an external drive via USB, FF14 doesn't even like being installed on the non-OS drive in a fair amount of cases....
I would suggest installing the game on the laptop onto the OS drive. If you don't have enough room, I suggest upgrading your OS drive.
You didn't give the make/model/year of your laptop, but if the OS drive is an NVMe SSD, then you defiantly want the game loaded on that as your load/zone times will be greatly reduced.

You might also consider shucking the SSD out of the Seagate One Touch and use it in place of the secondary HD in your laptop as an upgrade, just search online on How To disassemble your One Touch to remove and re-purpose it's SSD.