Plugin/Hack Required – Index and Search External Links & Anchor Text

I have a website that has a single page with a bunch of links to external pages that I do not own.

On the home page, of said website, I have a search bar.

If I enter in the anchor text for one of the links on the “Links” page, it returns a single result with the link to the “Links page”

What I WOULD like – if possible – is on the search page, to return actual links, from the Link page, that the user can click, that match the search query – rather than a link to the “Links” page.

Is this possible with ANY plugin? I’ve been banging my head into a wall for a couple hours on this now.

Thanks!