what may or may not be hard reality

So you should have clicked that so you made statistics.

Yep, RP does wear his watch on the right. A little research quickly garnered several more pictures of him with his watch on the right. He also shoots with his right which most likely (see how I said 'most likely' there, as opposed to took it for circumstantial fact like the shows?) makes him right-handed, but no actual pics of him writing.