Unfortunately not I pestered EVA repeatedly on their FB page for an answer, but they would not even answer the question.

The arrivals showers for the public are in the baggage claim area, and this is an option, or if you want to do the transit routine before clearing immigration, the rather gross transit hotel has a shared shower facility, or for more money, a private room with shower.

Another far more aggravating option is buying a separate refundable ticket on EVA that departs well after your inbound TPE arrival and use that ticket to get into the lounge, then after finishing, refund it.