I'm right handed, left eye dominant. Started shooting right handed because I didn't know any better, switched after about 5 years, first with shotgun then rifle a few years later.
I don't put too much thought into the ejection port, I care about controls. Some guns are fine left handed, others suck. Safeties are a big one, cross bolt safeties suck from the wrong hand for instance.
Bolt action rifles I much prefer left handed, especially for things like hunting where I am likely to be cycling the action from the shoulder. Shooting a right handed bolt gun from a bench is one thing, I do it all the time, but in the field I much prefer a lefty. My only dedicated left hand guns are my Rem700 hunting rifle and a bolt action 22.
Shotguns I mostly don't care - my most used shotgun is a Mossberg 500, with its tang safety its pretty ambidextrous. My semi auto has a cross bolt safety but I generally use that gun in situations where I'm either not using the safety or have plenty of time to take it off (trap range, duck blind, etc).
My only single shot rifle is a Henry, its completely ambidextrous.
I shoot a lot of 22s that are right handed. My right forearm gets burned by powder or hot brass occasionally in T-shirt weather, and a lot of them use safeties that aren't conducive to left-hand use (crossbolts, or things that aren't easily reached from a left hand grip) but there aren't a lot of 22s that are lefty other than bolt actions. Winchester Wildcat has a reversible safety and ambi mag release, but its still Right-side eject. Thats the closest I have to a lefty 22 that isn't a bolt gun.
Long story short, a lot of the time I'll just put up with RH guns, but I do prefer a lefty when its an option. Ejection port side is pretty low on my list of why I like a lefty though.
My daughter is left eye dominant and right handed. When she first picked up a rifle she wanted to hold the rifle right hand and sight with her left eye. That obviously doesn’t work and it was easier for her to shoot left handed. My brother is the exact opposite and he shoots right handed like any other right handed shooter would. I know I’ll get blasted for this, but it’s not just a matter of closing one eye. You aim where you naturally look. Your dominant eye leads you to that location.
Obviously this is much easier for a younger person to adapt to. But I have a cousin who lost the vision in his right eye earlier this year and is now shooting left handed like it’s how he has always done it.
Closing one eye is fine if you're shooting a scoped rifle from a bench. It is not a good solution for shotgunning or using iron sights though. Its also a recipe for headaches and fatigue if you spend any amount of time doing it. I closed one eye for years, and at least for me, switching sides was a game changer, especially with shotguns and iron sights.