WWW::Mechanize is a subclass of LWP::UserAgent, and like WWW::Mechanize::FAQ explains, they don't do javascript, use WWW::Mechanize::Firefox or WWW::Mechanize::PhantomJS for javascript

mechanize javascript -> WWW::Mechanize and buttons tied to javascript

Win32::IE::Mechanize will support javascript if your version of internetexplorer supports javascript... just click the button or link (as documented) ... IE::Mechanize/IEAutomation... same kettle of Win32::OLE/MSDN info, see Re^3: How do I add a timeout to Win32::IEAutomation click method for tips