I finally found an answer! The first thing you need to do is to create a search results page. The search results page will have a title something like "Search Results," and the following two lines in it:
where X is the number of a library that contains all your link categories.
Next, go to that page. When seen on its own (not as a result of a search), it will have a complete list of all your links. Ignore that, because no one will ever see it. Now view the source of that page. There will be a bit in it that will read something like this:
<form method="get" id="llsearch">
<input onfocus="this.value=''" value="Search..." name="searchll" id="searchll" type="text">
<input value="2003" name="page_id" id="page_id" type="hidden">
<input value="Search" type="submit">
where the input value for the page_id will be your newly created page. Copy and paste all of that code into any page in which you want to have a form to search links, and save the page. Voila! You will have a search form that will search all your links, not just the ones on the page on which the search form is located. When someone uses the form, it will take them to your newly created Search Results page. However, the list of all the links will not appear on that page when it is found through the search function. Instead, that page will have only a search box and the results of the search.