The situation you encountered is normal, because the website of the Taiwan Intellectual Property Administration charges a fee and cannot be searched by individuals. It is recommended that you ask a local Taiwan office to search for you.
Our firm handles a large number of Taiwanese patent applications every year, many of which are in the situation you mentioned. If it is a utility model, since the Patent Office of the State Intellectual Property Office does not conduct substantive examination, it can obtain the patent right. If it is an invention patent, the problem of prior application will be encountered during the substantive examination process. Then we need to analyze specific issues in detail.