The SA Scottish -- officially the 4th SA Infantry Regiment -- existed only in WW I, and it wore metal shoulder titles consisting of a springbok's head between thistles over the name "South Africa". It was known as the "SA Scottish", not "SA Scottish Regiment".
I agree that this cloth title is unlikely to have been theirs. If it is, then it must be over 100 years old.
IIRC, the Rhodesian SAS unit was called "Special Air Service Regiment" in the 1970s. Perhaps the cloth title comes from there.
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Regards
Arthur
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