Not sure exactly what you are doing, or did wrong before, but the way it works in the game is one side of each gi string is grounded to turn on the lamps, the other side of each string is always 6.3vac. The strings controlled by triacs vary the ground basically, so they can turn on full ground for full brightness or zero ground for no brightness of the bulbs.
J115 pins 1,7,8,10,11,12 are all ground pins. In you disconnect pin 1, that would leave all the triacs without a ground, and I doubt any string would light. The other ground pins each go to one triac, so I believe if any of them were disconnected that string would not work.
Of course the other pins on J115, pins 2,3,4,5,6 are all power at 6.3vac all the time.
If you wanted to wire an aux transformer to power all the strings at once, you could by wiring one side of a 6.3vac to pins 1,7,8,10,11,12 and the other to pins 2,3,4,5,6. If many bulbs were going to be lit though it would take a large transformer.