How can I convert a non-ICAO (Taiwanese) pilot's license to FAA or EASA?
I can't tell you anything about the EASA regulations, but there seems to be no way to convert a non-ICAO license directly to an FAA one. 14 CFR 61.75 says (my emphasis):


  (a) General. A person who holds a foreign pilot license at the private pilot level or higher that was issued by a contracting
  State to the Convention on International Civil Aviation may apply
  for and be issued a U.S. private pilot certificate with the
  appropriate ratings if the foreign pilot license meets the
  requirements of this section.


As you said, Taiwan is not a signatory to that convention, so the FAA can't issue a license under 61.75. (61.153 allows converting a foreign ATP license to an FAA one, but it also requires that the license come from a contracting state.) I couldn't find any special regulations or exemptions for Taiwan on the FAA's site.

You said that you know people who have "converted" a Taiwanese PPL to an FAA PPL, but do you know exactly what they did? My guess is that they applied for a regular FAA license, and used their flying time in Taiwan to count towards it.