arumics is the best way to gain union points by doing the luxemtower quest. It always comes up every hour. It starts whenever one of the arumic members is shouting this quest in Junon. The quest is to deliver something to lutis in luxemtower(he is on top of the tower-old guy). The best way you can do it is to buy lots of zant and junon scrolls to maximize your time. The most you can do it from what i heard is 5 times each hour if you are fast enough. You get 5 points everytime you hand it in.
Eqiupment that have moving speed are wings, eagle beak(25), devil wing bat(60), boxing boots and ideally have 5 moving flames
I hope this helps u a bit rootie ^^