From what I can gather from this newsclip. The Taiwan Railway Admin has decided that you can now take on board folding bikes at no extra charge on TzeChiang, FuShing and ChuKwang trains. You must fold them up like luggage, and this right may be suspended during major holidays. This includes the trains on both the west coast and east coast but does NOT include the Taroko Express trains or the old type TzeChiang trains (doors are too small).
Previously only allowed on the normal commuter trains (where apparently all bikes are allowed?)