AWS Rekognition Detect Eyes And Direction

Rekognition does not provide any functionality to detect the direciton of the eye.
Rekognition detects the eye open as an attribute which could be useful.
https://docs.aws.amazon.com/rekognition/latest/dg/API_FaceDetail.html#rekognition-Type-FaceDetail-EyesOpen

Regarding face turned to side, Pose attribute from face detection API could be used.
https://docs.aws.amazon.com/rekognition/latest/dg/API_FaceDetail.html#rekognition-Type-FaceDetail-Pose

Amazon Rekognition is capable of detecting faces from different perspectives and giving you the bounding of all the faces in an image. But Amazon Rekognition is unable to do such a detailed analysis of the eyes, in that case I recommend you develop your own algorithm