# UNTESTED; USE AT YOUR OWN PERIL :-)

my $response = $mech->submit_form(
        form_name => 'loginForm',
        # ...
);

  # Follow HTTP or META refreshes.
if (my $url = $response->header('Refresh'))
{
    $url =~ s/^\d+;url=//i;
    $mech->get($url);
}