SSIs don't work from within Perl scripts (least I've never known them too). They only work within static documents, because the web server, when it gets a request for a Perl script, hands off control to perl, which is then expected to basically just write its output back to the client.

The server doesn't actually parse the HTML written by the Perl script (as compared to when you use SSIs in a server-parsed HTML file, when the server parses the file to find any SSIs), so your SSIs won't get expanded if you try to include them in the HTML outputted by a Perl script.