I assume that when the British Invasion of the 60s spread to America, it also spread to other Westernized places that were somewhat British in culture (such as Australia) and this would include Rhodesia. So did the British fashion of rock music infect the scene of Rhodesia? What, exactly, was “the scene” in Rhodesia, for that matter, among the teenage and 20s set? Were the Beatles extremely popular there, or were there Rhodesian rock bands in the “British Invasion” style which were unique to that country? There would have to have been some, right? What were some examples of them?
I realize it’s fiction, but James Michener’s novel The Drifters takes place in approx. 1973 (IIRC) and discusses young adults traveling through Europe and Africa. There is a great deal of discussion about music and how it affects the culture of these young adults. (It’s also a damned good book, IMHO.)
Given the amount of research that Michener is known for putting into his books, it might at least give you a cultural reference.
I don’t know about local bands, but they’d certainly have listened to South African bands of the period too. Stuff like Four Jacks and a Jill, Clout and Rabbit. Note that there were some Brit Invasion elements that were South African, like Manfred Mann.