I have found that the easiest way to check on availability is to simply call EVA and ask them if there is an upgrade available for the specific date/flights. They are very helpful. You will need a B/Y class econ fare or a L? (or K, I can't remember which) to be eligible for an upgrade. A T class ticket will not be eligible unless you want to pay cash at the desk when you check in (and it will be a lot).