Both the product and page links are out put by the [-- SEARCH_RESULT --] tag. In your code you have that tag always being used. What you need to do is output it in the case of a product and ignore it in the case of a page link. Something like this should work.
Edit the [--DEFINE LINK_TO_PAGE--] section of the template specified on the Preferences > Search Settings > Search Layout > Link Template Override: and remove all tags so you just have
[--DEFINE LINK_TO_PAGE--]
[--END_DEFINE LINK_TO_PAGE--]
Note you may want to create a special page template with just that info to use for your search link template.
I finally got it. But here's the trick. Using shopsite pro v10, the Search Destination setting on the Edit Product Info screen must be set to "Store". Jim said to turn it to anyting but "More Info". I tried None and that takes it out of search entirely. Made creates a page not found error.
Store is the only setting that resolves this issue.