I can’t provide any documentation either, (see Malphono’s post), but I can say that I was instructed when I was ordained not to wear a ring at Mass. I was told that it was inappropriate, but that there would not be any negative consequences if I “got caught.”
The reasons are twofold:
- A ring is reserved to prelates.
- A ring is secular adornment, and as such it should not “show” when a priest is vested (prelates rings being a different matter of course). It’s like covering the shirt-collar with an amice–nothing but the vestments should be visible.
I remember that older priests used to remove their watches before Mass as well, although that might just be coincidence with no liturgical meaning whatever.
I also can’t document this, but I once heard that the Dali Lama said to Pope John Paul II that he shouldn’t wear his wristwatch at prayers, because prayer-time is not secular-time, and so it’s inappropriate to wear a watch while at prayer. I’m not saying that it happened. But whether it’s true or not, the idea does make sense.