For me, the card that stands out THE MOST when it comes to TWIN SOULS is the 2 of pentacles.
The figure 8 representing the eternal tie of the unbreakable connection. The waviness/unsure footing of the character of the card highlights all too well the confusion and uncertainty of twin soul separation and balance in connection.
The number 2 signifying reunion as well.. though as the card shows there's uncertainty, suprise, balance and inevitably change.
(and yea, the 6 of cups will often come up too and the Ace of cups and the sun)
For KARMIC relationships - often Justice comes up for me aswell as the chariot which highlights karmic aspects in the black and white horses that pull the chariot.
For SOUL MATE relationships - the two of cups, six of cups, ace of cups, the sun.