Whether sideboxes or just hardcoded links, the process of controlling the pages where they display is similar.

You can use a page test wrapping the code for processing the output, such as

if ($current_page_base != 'pagename') {
code to be hidden on pagename;
}

Or you can hide the output of an element which has a class/id tag for a certain page by prefixing #pagenameBody to the rule in the stylesheet:

#pagenameBody .linkGraphic1 {
display: none;
}