Fawkes was soaring around its head, and the basilisk was snapping furiously at him with fangs. From this we can see, that Fawkes did not really sneak up on the Basilisk from behind (reaction of @ash_k29 comment), it looks like Fawkes really had to be careful not to be hit by the fangs. For this part I think he would need to have open eyes, so ... More @Wikipedia
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