Basilisks will not use Stone Gaze if only one character is active. If multiple characters are active, Basilisk will always use Stone Gaze on its first turn; however, in a battle with multiple Basilisks, this only applies to the first one to get a turn.
As Funguars that often accompany it cast Fire, a strategy that the party can employ is to summon Ifrit as he is healed by Fire-elemental attacks and is immune to petrification. An alternative is to use Blizzara or Blizzaga, as Ice does the most damage compared to the other elements.
Basilisk is a fictional beast that appeared in medieval bestiaries, it is said that a single gaze to their eyes would kill or petrify the observer. It was supposed to appear when a chicken's egg was hatched by a snake or a frog (hence their reptilian appearance).The