Toggle Function Keys in System Setting

AppleScript
#1

Hi,
I’m currently attempting to toggle the function keys in the system settings on macOS Ventura 13.3, i can’t get it to perform a button press (Toggle).

AppleScript 
tell application "System Settings"
activate
reveal pane id "com.apple.Keyboard-Settings.extension"
delay 1
tell application "System Events"
	tell process "System Settings"
		click UI element 12 of group 2 of scroll area 1 of group 1 of group 2 of splitter group 1 of group 1 of window "Keyboard"
		delay 1
		tell outline 1 of scroll area 1 of group 1 of splitter group 1 of group 1 of sheet 1 of window "Keyboard"
			select row 11
			delay 0.3
			tell UI element 1 of row 11
				click button 1
			end tell
		end tell
	end tell
end tell
end tell
Automator 
on run {input, parameters}
	-- Click the text “Keyboard”
	delay 1.882038
	set timeoutSeconds to 2.0
	set uiScript to "click static text 1 of window \"Keyboard\" of application process \"System Settings\""
	my doWithTimeout(uiScript, timeoutSeconds)
	
	-- Click the “<fill in title>” button.
	delay 0.926165
	set timeoutSeconds to 2.0
	set uiScript to "click UI Element 12 of group 2 of scroll area 1 of group 1 of group 2 of splitter group 1 of group 1 of window \"Keyboard\" of application process \"System Settings\""
	my doWithTimeout(uiScript, timeoutSeconds)
	
	-- Click the “<fill in title>” button.
	delay 1.720122
	set timeoutSeconds to 2.0
	set uiScript to "click UI Element 1 of UI Element 1 of row 11 of outline 1 of scroll area 1 of group 1 of splitter group 1 of group 1 of sheet 1 of window \"Keyboard\" of application process \"System Settings\""
	my doWithTimeout(uiScript, timeoutSeconds)
	
	-- Click the “<fill in title>” checkbox.
	delay 1.374169
	set timeoutSeconds to 2.0
	set uiScript to "click checkbox 1 of group 1 of scroll area 1 of group 2 of splitter group 1 of group 1 of sheet 1 of window \"Keyboard\" of application process \"System Settings\""
	my doWithTimeout(uiScript, timeoutSeconds)
	
	-- Click the “<fill in title>” button.
	delay 1.292147
	set timeoutSeconds to 2.0
	set uiScript to "click UI Element 2 of group 2 of splitter group 1 of group 1 of sheet 1 of window \"Keyboard\" of application process \"System Settings\""
	my doWithTimeout(uiScript, timeoutSeconds)
	return input
end run

on doWithTimeout(uiScript, timeoutSeconds)
	set endDate to (current date) + timeoutSeconds
	repeat
		try
			run script "tell application \"System Events\"
" & uiScript & "
end tell"
			exit repeat
		on error errorMessage
			if ((current date) > endDate) then
				error "Can not " & uiScript
			end if
		end try
	end repeat
end doWithTimeout
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#2

The answer seems to be in this code:

If I understand the code correctly, you can change the state of the function keys by using this command:

defaults write -g com.apple.keyboard.fnState 1

1 turns on F1,F2, etc. as standard function keys; 0 sets them as special-purpose keys.

And the part that I don’t know how to accomplish from the command line or AppleScript is the notification to the system that the Fn key state has been changed. In the Xcode project, that seems to be here:

NSDictionary *dict = @{@"state": @YES};
    [[NSDistributedNotificationCenter defaultCenter] postNotificationName:@"com.apple.keyboard.fnstatedidchange" object:NULL userInfo:dict deliverImmediately:YES];

Is there a way to send this notification via AppleScript or any other way?

EDIT: There seems to be a way to do this here, but I don’t pretend to understand it, or how to adapt it for this situation:

EDIT2: Unfortunately, the fntoggle utility doesn’t change the state returned by defaults read -g com.apple.keyboard.fnState - that command will always return the setting shown in System Preferences, which doesn’t change when the fntoggle utility changes the actual state.

#3

I was able to toggle the fn function key using the shell script, but unfortunately, that doesn’t actually change its state as you previously mentioned. That’s why I opted to use the GUI way.

use AppleScript version "2.8"
use scripting additions

set fnState to do shell script "defaults read -g com.apple.keyboard.fnState"

if fnState is "0" then
	do shell script "defaults write -g com.apple.keyboard.fnState 1"
	set notificationTitle to "fn Function Key On"
	set notificationSubtitle to "The fn function key is now ON."
else
	do shell script "defaults write -g com.apple.keyboard.fnState 0"
	set notificationTitle to "fn Function Key Off"
	set notificationSubtitle to "The fn function key is now OFF."
end if

display notification notificationSubtitle with title notificationTitle sound name "Pop"
#4

Yes, but as you know, the notification in the fntoggle executable isn’t the “notification” in an AppleScript that displays in the upper-right corner of the screen, but an internal notification to the system so that it puts the change into effect.

#5

I’m not sure this is progress, but I think I very dimly see that the script to turn on Fn1, F2 act as function keys, and send the notification to the system, might look something like this (THE ALL-CAPS STRING IS MY GUESS AT WHERE I NEED TO PUT SOMETHING USEFUL):

And since I have no idea of what I’m doing, it’s probably best just to ignore me…

use framework "Foundation"
use scripting additions
property parent : class "NSObject"

do shell script "defaults write -g com.apple.keyboard.fnState 1"

set noter to current application's NSDistributedNotificationCenter's defaultCenter()
set dict to current application's NSDictionary's dictionaryOFSOMEKIND???
noter's postNotificationName:"com.apple.keyboard.fnstatedidchange" object:(missing value) userInfo:dict deliverImmediately:1