Hill arrived in South Africa at the beginning of 1902, so he had missed out on all the battles that the famous Highland Brigade had fought from their deployment in 1899, which, of course, certainly is not a bad thing, as so many were never to see home again.
The closing months of the war were and are considered by some, including me, to be the worst, the war had entered a new and brutal phase with the enemy being hunted down by specialist anti commando units on the veldt and being driven into the hands of the British Armies blockhouse lines.
Interestingly, Hill did not leave South Africa until the beginning of 1903 and was part of the garrison that remained to enforce and back up Lord Milner's new administration, after his actual wartime service, which included time spent in the Transvaal which could often be very dangerous indeed, depending on exactly where one happened to be, I would think he had been up in Klerksdorp, so he would have needed eyes in the back of his head, dark days for so many, sadly!