Since WebService::Simple->isa('LWP::UserAgent') you can use

$google->add_handler("request_send",  sub { shift->dump; return });
$google->add_handler("response_done", sub { shift->dump; return });
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I was going to suggest you use the WebService::Simple->new( debug => 1 ...) option, but it wouldn't have helped. I would switch to WWW::Mechanize (or WWW::Mechanize::Cached), its much better in all respects.