Couldn't find much on this other than what I've quoted below. But, in my opinion, I think the name of the shirt is misleading and was the reason I even bothered to look it up.
❝This is said to give bonus points to your tally for prizes when worn during the event.❞
Looks like it was used in 3 different events or was introduced and used in one event but also would be useful on 2 other events. This is just my guess anyways without looking up the details of each event. Listed the 3 events below.
❝Let's Go! Vana'diel Day! - May 15th 2018, from the Goblin Rejoicer or the Treasure Coffer (Anniversary).❞
So, looks like this shirt is basically worthless outside the events unless you want it for looks. My self, I can think of much better things to fill up my valuable inventory space with than this NOTHING Nabber Shirt. ~.^