EVA has four lounges that I know of at TPE - star, infinity, garden, and club - but they are all at departure level. I don't believe you will be able to access them on arrival, unless you are transiting onward.
There is nothing at all that prevents a pax from going upstairs even when not transiting. The transit security checkpoint does not care about onward tickets, and there is no check at all when returning downstairs
That said, I have no idea how much luck they will have with the lounge dragons.
EDIT: Just saw the above link to a post by bocastephen where they told him to pound sand trying to get in. No reason to disagree with him, the only time I got in as an arrival was when I was BR Diamond.