An update to this topic for the first time since 2015.
A friend has now discovered that my paternal grandmother died on 15 February 1937 according to the South Africa Transvaal Civil Death, 1869-1954 records. She died in the Johannesburg Hospital after being there for 9 days suffering from Otitis Media Terminal Acute and Pneumococal meningitis aged 42. She was divorced and living at 42 Anglo African House, Joubert Street, Johannesburg and is apparently buried in (what was known at that time as) the New Cemetary in Johannesburg. The number of the entry was 1335 but I haven't been able to find this on FindAGrave.
Any further information appertaining to her, Gladys Harvey Pezzey Southwick would be very gratefully received - thank you.