The stole should be worn when any sacrament is done. Of course, it’s lack would not invalidate the sacrament. In our parish, a stole is kept in the priest’s station in every confessional so as to be readily available.
I always go behind the screen (haven’t felt the urge to go face-to-face yet), so I couldn’t even tell you most of the time whether the priest was wearing it or not.
Entirely true.
The Sacred Congregation of Rites has given a large number of decisions concerning the use of the stole. As a general rule it may be stated: the stole is only used, and must be used, at a function peculiar to the deacon, priest, and bishop, a function that presupposes the order (e.g., at the celebration of Mass, when the Blessed Sacrament is touched, when the sacraments are administered), but not for example, in processions or at Vespers. http://www.newadvent.org/cathen/14301a.htm
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