Practice till you get it wrong... short sessions where you think you are doing good do nothing for you in the long run. Longer sessions fatigue anyone... what matters is your ability to perform under that added stress... whether in competition, a long day of hunting, or in combat.
Like others said, you can help by throwing some medical tape on your shooting glasses. I have the opposite of you, shooting an AR or handgun two eyes open is fine and feels natural, sometimes when behind a scoped rifle I want to close an eye, but I found the tape helps get over that. Now I can shoot two eyes open with a scope with out much thought.
If you are out doors, and long sessions... especially in the sun... bring a snack... nothing huge that will weigh you down, but a granola bar or something, and hydrate. It sounds stupid, but it can make all the difference in the world. I was at work for a range event in the high summer heat and humidity on the shooting range for nearly 10 hours. You couldn't give me enough water or gatorade that day. At some points I found it very hard to focus on my sights or targets when I started to feel hungry or dehydrated.