First you had a typo in the .dropdown-toggle
class.
Then you are not looking for a vertical separator that will look like a border, but for a border, and you just need to hide some of them.
Here is your key:
.navbar .nav > li > a.dropdown-toggle { position: relative; bottom: -1px; z-index: 1005; background: white; padding-bottom: 12px; } ul.nav li.dropdown:hover ul.dropdown-menu { border-top: 1px solid #000; }
padding-bottom
is actually just one more pixel than the default.
Another important thing is the position on the left or right:
ul.nav li.dropdown:hover ul.dropdown-menu { left: 0px; }
I fixed a few other things to improve the effects, but you have a basic idea.
Updated jsfiddle
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