Assuming you're actually looking at one of the FFXIC_CHRxxxxxxxxxxxxxxxx folders in %USER% > Documents > My Games > FINAL FANTASY XIV - A Realm Reborn, the folder modified date of the folder may not change, but the .DAT files in that folder should have updated modified dates. Changes to the HUD should cause a change in the modified date for at least ADDON.DAT.

I run two accounts each having multiple characters on two machines, and a character can be on either the main machine or the second machine depending on what I'm doing, so I copy my UI, keybindings, etc a bit, both between machines (using a USB stick) and between characters.
The files I copy to copy the UI from one char to another for from one machine to another are:
ACQ.DAT: not sure what it does
ADDON.DAT: UI setting including HUD layout
COMMON.DAT: settings located in Character Settings menu
CONTROL0.DAT: Keyboard/Mouse Setting
CONTROL1.DAT: Gamepad/Controller Setting
HOTBAR.DAT: Contents of Hotbars but not Hotbar positions
KEYBIND.DAT: Key bindings
MACRO.DAT: Title, Icon and Line list of custom macros for character.
LOGFLTR.DAT: Chat log filter and color settings.
I got this info from https://eremiss.tumblr.com/post/6344...xiv-pc-version

A tip for alt lovers: once you've figured out which FFXIV_CHRnnn folder is for which character, create a text file named after the character in that folder (e.g. "bunvivant.txt") so you don't have to figure it out again later.

Note that you can also save a character's settings to SE's servers as an option on the character-select screen once you are logged in, and then restore those settings later (to the same PC or another PC) from the same screen.