New sidebox – can I edit links from Links Manager?

I’ve added a new sidebox (which I’m calling ‘External Links’) to my sidebar by copying the php code from the original ‘Links’ sidebox and changing the new sidebox’s title, but I can only get it to work by typing the links’ URLs into the sidebar.php file.

Is there any way to edit the links shown in this new sidebox by using the Links Manager instead of editing sidebar.php?

So far, I can see the title of my new sidebox in the ‘Category’ dropdown menu in the Links Manager but anything I add to it automatically gets added to the original ‘Links’ sidebox as well (which is the sidebox I copied the php code from).

It looks like it’s possible, but I can’t get it to work.