I think I may have a more elegant solution for you:

#!/usr/bin/perl -w
use strict;
$|++;

BEGIN{
    use CGI qw(:standard);
    print header;
    print start_html;
    print "Please wait";
    print end_html;
}

sleep 5;  # Code that process form would actually go here

require Perl_file_that_redirects_browser_goes_here.pl;

# Above line simply calls a Perl file that uses CGI.pm "redirect" func
+tion to redirect the browser to the desired page.
[download]

This is untested but I don't see a reason why it wouldn't work.

Update: After some testing, this isn't working because the redirect gets printed to the HTML page instead of redirecting the browser because it is called after the content header. I naively assumed using calling another script with "require" would solve this problem but it doesn't. Anyone else have any ideas on how to redirect the browser?

$PM = "Perl Monk's";
$MCF = "Most Clueless Friar Abbot";
$nysus = $PM . $MCF;