Could you add a little desktop window (floating) that could be displayed as permanent window on the desktop. The additional window shall display a selectable number of tags in a list (preferable those that are already pinned).
When someone clicks an list item representing a tagged time it starts the stop watch, if i click again it stops the stop watch and inserts the expired time with the tag clicked. Using this method some clicks that i currently need to do to start the stop watch via task menu.