Out of curiosity, I went back to look at some of my old images, and I shot my vertical formats BOTH right side up, and right side down.
So it was indeed a case of whatever felt better and more stable to do at the time, with whatever lens was on the camera.
The particular orientation (right side up, and right side down), may also depend on the layout of the individual camera and lens.
The situation also affects the orientation. As I mentioned earlier, rapid shooting events, required right side up, so I could work the film advance lever fast.
Your body may also affect this. I can hold steady both right side up and right side down, because I was trained to. Someone else may not be able to hold steady right side down. So you do what works for YOU.
IMHO, the main thing is that the supporting hand (left or right) be supporting the weight of the camera+lens at the appropriate place for balance and max stability, be it under the body (with left or right hand) or the lens (with left hand), with fingers on the focus ring to do focus tracking. And using proper technique to hold steady.
Oh, my father's Exakta had a WLF, so shooting vertical was a real PiA, so I very rarely did it. Think about it.
My opinion, do whichever works best for YOU and YOUR GEAR, and shoot film
