So, I was reading this thread, not understanding how two eyes could possibly be better than one. I mean, how could anything be better than three points that form a straight line, eye, compass hairline, and target. If you add a second eye to the side, it could only make things worse [not counting empirical examples in which "real life" complicate theory, and there, all bets are off].
I tried reading the Compass and Tape article and it more or less agreed with me, but I zoned on it. So I downloaded a Suunto manual and it said this:
With both eyes open, aim the compass so that the hairline is superimposed on the
target, when viewed through the lens. The main scale (large numbers) gives the
bearing from your position to the target, the small numbers give a reverse bearing
from the target to your position. This feature is of great assistance when calculating a
precise position.
Use the left or the right eye as preferred. With both eyes open, an optical illusion
makes the hairline appear to continue above the instrument frame, superimposed on
the target. This improves reading accuracy and speed.
So now I think I understand. *If* you can make sure the hairline is directly above or below the target, you're golden. The problem comes in that the target and the hairline aren't super imposed (except in folding mirror style compi). So, it all depends on if the error you generate by trying to look into the compass and at the target is greater or less than the parallax issue of both eyes open. Suunto seems to think the parallax is the lesser of two evils. I would think that depends on the distance to the target and the skill of the instrument reader. And various other things like the awkwardness of the station.
So, an experiment is an ideal thing to do, to see which is better for any individual.