Been looking at pics from the UK HFT shoots, some guys have both open the some are doing the wink. From what I've researched it's best to keep both eyes open to delay fatigue. Finding it a bit difficult myself though.
To avoid eye strain, aid in overall balance and to keep the same amount of light reaching both eyes it is important to keep both eyes open.
I learned this in the 10m discipline where you wear a peak and use a thin strip of cardboard or tape or hazy plastic in front of the non-shooting eye.
This allows peripheral vision to the non-shooting eye which aids balance, it allows some light to reach it and does not allow it to focus on anything thus not disturbing your sight picture....
Try it...you will be amazed..
I was never forced to use both eyes when shooting as a "sniper" in my army days.It was a choice.How anybody can look through a scope with one eye only and stillstan up is beyond me. I fall over because everything is heywire. I will go along with Quido's bit about balance etc.,it sounds logical.Taking long shots (sniping)equires a lot of concentration and I would/did not ever, even think of doing "rondom opserwasie" in the same time as aiming at something/body."Observe, shoot, observe again and get out of there" was our moto in the good old S.A. Army, I don't know in other countries.
When I started shooting wayback when, the guy who taught me was an old Springbok bisley shottist and the first thing he did was determine which was my dominant eye. As a result I learnt to shoot left handed. I have no problems with balance etc. and am only slightly aware of peripheral vision if I specifically look for it. But let something move or enter my area of peripheral vision and I am immediately aware of it. A big advantage of shooting with both eyes open.
There was an article about this issue in a Magnum magazine in the past year or so. Can't remember exactly what the detail was, but I seem to recall that the author said something along the lines of do what you feel comfortable with. I have lately been trying to shoot left handed, because of problems with vision in my right eye and let me tell you, its not easy. Will get there, eventually. It still feels funny at this stage.
There is a little known problem, except to opticians, called heterophoria which is a mis-alignment of the eye axis. Try this, look through your scope with both eyes open then close your "non scope eye". If the object your looking at moves slightly then its the "Long John Silver" look for you.