The message
from Stuart contains these words:

I trust that the wall in question is constructed out of studwork rather
than flimsy battens.

Dunno what the definition of a "batten" is but surely it could be made
of 2" x
2" . We don't know if the OP's wall is a self standing construction or
if the
battens are attached to an existing wall so if the latter then 2" x 1" could
well be sufficient to support the PB .

I think 2" x 2" is is oversize for a batten, particularly in thickness,
but you could be right about the construction in this case; dry lined
external wall rather than studwork interior wall.

batten

Concise Oxford

1 a long flat strip of squared timber or metal, esp. used to hold
something in place or as a fastening against a wall etc.

Collins

1 a sawn strip of wood used in building to cover joints, provide a
fixing for tiles or slates, support lathing, etc.


--
Roger Chapman