The "Border on all menu items" context help says
Every item of the menu bar, plus the menu bar itself, will be wrapped into this border. To have no borders in the first level, give it the same color as the background color for first level items. Don't use semicolons here.
When I added "solid 1px #cccccc" here, it put borders around the menu items but not around the entire bar (which is the same color as the menu items). How might I get a border around the entire menu bar?