IMO, both eyes open, especially when hunting, especially when in the timber when a shot on a game animal presents itself. I find when I bring the rifle up with both eyes open, the rifle comes up and naturally puts the scope's "hairs" exactly in line with my vision, exactly on the animal; no "hunting" hairs this way when the heart rate likes to rise a bit...
Practice looking/scoping at a specific target; rock, stump and etc., with both eyes open until you've developed this technique; doesn't take long, really, and I've found it's like riding the proverbial bicycle, and it doesn't matter if it's 50 yards or 300. You can do this practice at home with a safe, empty rifle (of course), too; back yard, garage, even in the house to prevent a nosey neighbor that might give you "both eyes" whilst dialing 911. Hopefully not, HA!
I got to shoot a very high-end ($$) long range competition bench rifle not long ago, and to shoot it right one needed both eyes open just to use both levels on the scope. That was a different process there, but I was fairly comfortable with it because I always keep both peepers open when using a scope. BTW, I use both eyes on open sights, too; nothing I even have to think about anymore.