Touch bar widget: Trigger run script when touch button is touched to speed up alternative icon changes

Alternatively if you don't want to duplicate your script you can use the refresh_widget function to refresh the widget with the given UUID, this will then run the widget script again immediately (also by assigning the "Run Apple Script" predefined action):

tell application "BetterTouchTool"
refresh_widget "2F34005D-4537-464D-94E9-A7F42DA39DF1"
end tell

See https://docs.bettertouchtool.net/docs/apple_script.html