You should print the return value of $stream->get_text('/ul');. There are examples in the documentation for HTML::TokeParser.

If all you want to do is dump the object, you can print Dumper $stream; while using Data::Dumper, but I don't think this will really tell you what you need.

Update: What you're probably missing in TFM is that the way you're using get_tag('ul') simply sets the parsing pointer to the first <ul> tag it finds, but doesn't capture the subsequent text. get_text('/ul') will capture all of the text from the current position (the current <ul> tag) until the </ul> tag is found.