Everyone agrees that Taiwan's government agencies need to do a little more (or a lot more) to make the country really tourist-friendly. Here's an example from Penghu. At the entrance to Yuwengdao Lighthouse (漁翁島燈塔, pictured here) in the Penghu Islands there are various signs. One says, in English and Chinese, 'No Entry'. Another, just below, states 'Welcome (Admission Free)'.
So, is this lighthouse open to the public or not? It seems to be. No one stopped us, or the Taiwanese sightseers there at the same time, from wandering around the grounds.