Hello fellow FF nerds, I'm posting this in the hopes it might save someone else a few hours.
I use Windows 10 and an Xbox 360 controller. By default, Windows 10 will automatically install drivers for the controller. With those drivers, all buttons will work in FFXI with the exception of the right and left triggers.
Long story short, to get the triggers working you'll have to install the
Windows 7 Xbox 360 controller drivers, which you can get from Microsoft here:
https://www.microsoft.com/accessories/en-us/products/gaming/xbox-360-controller-for-windows/52a-00004.
Be sure to download the 32-bit/64-bit drivers as appropriate (based on your machine).
In the "Final Fantasy XI Gamepad Configuration Tool" you can select "Alternate Setup E (E)" for an out-of the-box button setup that works. Alternatively, you can just make sure "Enable XInput" is ticked off in the Gamepad Options found in the top right and customize the rest of the options as you like.
What you don't need is any special third party driver, like XBCD, XPadder, or the Xbox 360 Controller Emulator (x360ce).
Happy gaming.