My right hand is all but useless, I'm very left handed. Golf is the only exception, but I'm terrible in either direction and right handed clubs are easier to rent or buy.
While in school, before WWII, he was beaten on the offending hand, to discourage him from writing with the left hand. So eventually he became accustomed to write with the right hand, and then he has continued to write with the right hand, even if he always did most other kinds of precision work with his left hand.
It took maybe a week to get used to the switch but wasn't that big of a problem even though I'm both left handed and left eyed.
So you just.. do it, I guess?
I had no idea until recently when someone said "Hey, you're doing that left handed"
I did pick up some ambidextrous habits. My daughter and I mouse with my right hand but my dad left handed a mouse.
(I do have clear preferences for many other activities, though which activities go left and which right seems pretty arbitrary, and might just be what I got used to instead of actual dominance. Like, I hold my phone on the right hand because it's in the right pocket, but is that a preference, or just avoiding putting the phone in the same pocket as keys/flashlight/etc?)
The reason I write right-handed is that my friend kept “correcting” me when we were learning. I still hold the pencil like a lefty, though, which gets funny looks.