I wasn't going to reply but something about this didn't attune with my memory of African Rock Pipit, but it was a while ago now that I saw them (and only around Sani Pass which is further east). One of the issues with all the pipits and the resources is looking for the right ssp and also local morphological differences which can be tricky in the published material.
However, the bird in the OP shows a pale bill and distinct dark centres to the median coverts - which African Rock Pipit shouldn't show.
Looking at the eBird Hotspot for Mountain Zebra NP there are a number of photos of pipits that occur there. A handy summary is the 9th Nov Checklist by Barry Reed
https://ebird.org/checklist/S201847889.
As to what it is - I agree with Fern that it looking short tailed which is odd for the options. The short answer is I am not sure - for example I cant work out if the back is truly unstreaked, the long answer is normally when I didn't know what they are in SA they turned out to be Nicholson's