the local range guru has got me starting to shoot with both eyes open. he never used to untill his vision started to fail, now he swears it helps keep his scope eye focused.
I dont suffer from eye fatigue like he does, however i feel much more comfortable during long shooting sessions with both eyes open. seems like my face is much more relaxed when both are open. i dont really notice an accuracy difference if my off eye is open or closed, only when my dominant eye is shut
like all things in life its different strokes for different folks. you'll get advice from both sides of the fence so do what works for you and run with it. just my .02.
then again i'm still a young shooter, maybe others know more.