The one that appears in the jungle spread of Hey, Rabbit! is more or less taken from the actual reptile.
(This one in the picture is from the Honolulu Zoo.)
According to Leonardo da Vinci, the basilisk likes to hide on the high tree branches and then stare at his (or her) victims as they wilt to death. That's not nice.
Other authors report similar behaviors, but if you look at my basilisk's face, would you believe she (or he) would be capable of such a thing?