Oops, well this is embarrassing

! (note to self; test before posting!)
I miss spoke, at least in part, earlier and the Oil brush head’s orientation is indeed already locked to a Pens rotation as it moves.
(Though for it to work the pen needs to be sending back it’s rotational information to AR.)
In AR 2 & 3, as noted by PRSS, the brush head would always orientate itself dynamically to the direction of travel. Whether using a pen, mouse or trackpad. The actual rotation of the pen was ignored.
From AR4 onwards, as I said above, this changed and the Oil brush started to automatically use the rotation of the pen to set the dynamic orientation of the brush head as it moved. So, effectively the same behaviour as when ‘Lock Rotation’ is enabled in the Knife tool.
In the absence of pen rotation information. ie when using a mouse or trackpad, the head orientation of the Oil brush in AR4 to 6, is now fixed and no longer changes dynamically as it follows the brush stroke.
It could be a very old bug that has just gone unnoticed for a very long time I suppose but I’m more inclined to think that it was changed by design.