You can check the components of the UI interface of the application you're trying to script with the "UI elements" command
tell application "System Events"
tell application process "System Preferences"
get the UI elements of the window "Keyboard"
end tell
end tell
you can then drill down the list to find where the required item is
tell application "System Events"
tell application process "System Preferences"
get the UI elements of tab group 1 of window "Keyboard"
end tell
end tell
actually using the Accessibility Inspector app (part of Xcode) can help you to identify which element to inspect
For our purposes, it looks like the popup we are interested into is the
pop up button 2 of tab group 1 of window "Keyboard"
Since it is a pop up, to interact with its menu, you have to click on it and then to select the item you want to activate. It can be done by specifying the whole label of the menu item to click, I preferred to simulate the keystrokes needed to switch the selection (either the up or down arrow and then the return)...
tell application "System Preferences"
-- activate
reveal anchor "keyboardTab" of pane id "com.apple.preference.keyboard"
end tell
delay 0.5 -- this depends on how fast is your mac
tell application "System Events"
tell application process "System Preferences"
set thePopup to pop up button 2 of tab group 1 of window "Keyboard"
tell thePopup
click
delay 0.2
if the value of thePopup begins with "App" or the value of thePopup begins with "Expanded" then
key code {125, 125, 125, 36}
else
key code {126, 36}
end if
end tell
end tell
end tell
quit application "System Preferences"
by the way, in another question, someone noticed that if you don't activate the System Preferences app, the scripts will still work but without showing its window (you will still see the popup menu being switched, though)