According to my understanding, it is a Roman adaptation of the
Epitrachelion and Orarion - essentially priestly neck-garments.
I wouldn't read too much into the clothing style itself, as it
changes infrequently and often erratically and illogically. But
the garment itself, functionally, is simply the symbol of the
priesthood or diaconate, but styled differently. It's also
important to note how simple they can be, so it is likely that
they were adapted as priestly garments some time after they were
in common use by aristocracy. The interesting part is that while
in the Orthodox tradition the stole is two different garments
for the priest and deacon, in the West it is almost the same
garment simply worn differently, albeit with the final effect
being identical: the priest's is symmetrical and comes down like
a beard, and the deacon's is asymmetrical and worn like a sash.
This suggests a common origin to all of the stoles, but does not
tell us what the proto-garment was, or if one of the two was the
proto-garmen