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...
my $response = $mech->get($url);
...
$logger->info("Clicking Sign in button");
$mech->click_button( name => 'signIn' );
...

 <form novalidate="" method="post" action="https://accounts.google.com
+/signin/challenge/sl/password" id="gaia_loginform">
  <input name="Page" type="hidden" value="PasswordSeparationSignIn">
...
  </div>
  </div>
  </form>