PAY: Gamble with Twinkbrix, win, and trade him an additional 2,000 gil.
To gamble with Twinkbrix, trade him an amount between 1-10,000 gil.
The amount traded will affect your chances of winning his dice game.
You have a 1-in-2 chance with 10,000 gil and a 1-in-2500 chance at 1g.
If 2716 gil is traded (corresponding to the number in Mine Shaft #2716) a secret message will be displayed. By trading this amount on a certain day, the chances of winning increase.
Winning the dice game against Twinkbrix only rewards you with the ENMitem.
After winning his game, trading him an additional 2,000 gil will prompt the Moblin to warp you to the shaft entrance.
TRAVEL: Have several party members zone through Newton Movalpolos and manipulate the timed levers to allow you to pass through. Then you must do the same for them, and navigate Newton Movalpolos by trading firesands to various gates to rotate furnaces. At (L-8) of Newton Movalpolos, you will find the Mine Shaft #2716 entrance.
NOTE: Option 3 is the the most time consuming; and may be problematic if not done correctly.