I had the same issue. With Stormblood, Square introduced a logitech applet for FF14. To resolve this issue follow these steps for a permanent solution. changing the setting in the settings window is only temporary in my experience as it resets itself when starting the game up again

1) make sure you logitech gaming software is up to date
2) open the software and where the devices are listed, scroll till you find the icon of a keyboard with what looks like a smartphone on it's side. This is the applet screen
3) select the ff14 applet in the left window
4) in the right window uncheck the box next to LED backlighting.