How old is the oldest Southern African rock art and can it definitively be attributed to the San? Is the art found in all areas that were once inhabited by the San or is it concentrated in specific places? Is it generally accepted that there was a continuous rock art tradition stretching from the Paleolithic into modern times? When did they stop and why? What do the current San say about this art? Do they feel it "belongs" to them and do they have narratives about what it depicts? What are some authoritative books or articles on the subject?
I can’t answer all your questions, but I can answer some. To start with, the San rock art tradition is truly one of the great artistic traditions of the world. There’s thousands of known examples all across Southern Africa from Central Namibia and northern Botswana (Twyfelfontein, Brandberg, and the Aha hills) to Zambia and Zimbabwe to the Cape. Though it’s concentrated in some places, such as the Cape and the Drakensberg, there’s some pretty much anywhere there’s suitable rocks. It’s hard to date rock art, but many paintings and engravings are certainly thousands of years old. The most spectacular art seems to be an innovation of the past 3-4 thousand years.
General features of San rock art are very (seemingly) naturalistic depictions of wild animals, especially antelope and especially especially eland, slender, silhouetted humans, therianthropes, or mixed human-animal entities, hunting scenes, and depictions of trance dances. The similarity between art that is thousands of years old to art that is hundreds of years old suggests that there is a continuous tradition, not just of art but of at least some of the spiritual and religious ideas behind the art.
So why don’t San make rock art now? The biggest (and saddest) reason is that the most productive San rock artists of the Cape and the Drakensberg have been annihilated, either physically (genocide; what happened to a lot of Cape San) or through cultural assimilation (many Cape San, whose descendants are now known as “Coloured”, and the Drakensberg San, who were assimilated into the Nguni and sometimes Sotho). The last independent Cape and Drakensberg San groups were assimilated in the late nineteenth and early twentieth century, though their descendants may still identify as San. Most surviving San are Kalahari San, who made some rock art in the past (Tsodilo hills) but didn’t have the tradition when anthropologists began studying them in the mid-twentieth century.
The destruction of the rock artists is the reason that the interpretation of the art is so controversial. The only major written record of the artist’s connection to rock art comes from Wilhelm Bleek, a linguist who worked with /Xam San (a Cape San group who lived in the area of present-day Calvinia) who had been imprisoned in Cape Town. At least one of the men he worked with was a shaman who explained the connection between rock art and the trance dances that are unique to the San. However, in the Drakensberg there’s also oral traditions among the Nguni and Sotho connecting the San to rock art. Despite the records, the depiction of very San trance dances, and the fact that the San were the only people around to make the art, as late as the mid-twentieth century Henri Breuil, an expert in European rock art, was saying that SA rock art was actually made by Egyptians and Phoenicians.
Your question about how modern San view rock art is really fantastic, partly because I don’t know the answer! I’m not aware of any work on it. The Kalahari San are the most intensely researched, but they lack the rock art tradition. So far as I know there’s been very little work done with Cape and Drakensberg San descendants. Recently in South Africa there’s been some reassertion of a Khoisan identity, but I don’t know if pride in the rock art traditions ties in to that.
As for books, David Lewis-Williams is certainly the most prominent writer; he’s put out big papers on the subject as well as books for a general-ish audience. Most of the information in this post comes from his book The Mind in the Cave: Consciousness and the Origins of Art. As you can tell from the title, he likes to make sweeping statements about the origin of religion and the importance of shamanism to human evolution. I don’t always buy it, but I think he’s a great source on San art and he’s well versed in Cape San history and Kalahari San ethnography (though he spells n/um “n/om”. I don’t know why). To be honest his more San-specific books are on my reading list but I haven’t gotten around to them yet!
Though it wouldn’t be very academic, I’d recommend finding a good coffee table book of San rock art. It’s really impressive!
