Appearance and Behavior Edit
While visually similar to Cockatrices Basilisks behavior is vastly different. They run around with medium-high speed to the point closest to them which allows them to fire indirectly at you, trying to avoid having obstacles in their path before they shoot.
Even if this seems logical to you, not every enemy behaves like that.
They also stay at that point until you move behind something, are out of range, they get hurt in any way or if they have already shot at you (they shoot at least once before moving after getting hit). Then they move to the next best point which is at least a few feet away from their current position before they shoot again.
Basilisks spit green acid projectiles in a grenade-like arc with medium speed and high precision at you, leaving a pool of acid underneath you dealing more damage over time.
Never stay still in a fight with them.
They have low health and are easy to hit, so using any weapon with high damage in a single shot takes them out quickly one by one (spell books like Hellish Ember work the best here).