The 6 clasps he received for his Queen's South Africa medal are listed on his records as:
Transvaal, Orange Free State, Cape Colony, Laing's Neck, Relief of Ladysmith and Tugela Heights. Each is described here:
https://en.wikipedia.org/wiki/Queen%27s_South_Africa_Medal The QSA covered service in the period between Oct 99 and May 02. He served there 12 Oct 99 to 14 Jul 00 and then again from 5 Mar 01 to Feb 06 (ie staying on after the war which ended in May 1902).
For the service after the end of the war and the length of his service in total, he qualified for the King's South Africa Medal which had 2 clasps as you see on the picture. Described here:
https://en.wikipedia.org/wiki/King%27s_South_Africa_Medal#Clasps.
His service in summary was:
Signed on for 12 years in 1898 consisting of 7 years colour service (ie active service) followed by 5 years on the reserve. There was a caveat that if he was overseas when the 7 years were up, the engagement could become 8 and 4. He could elect to do 8 and 4 himself.
In 1904 he elected to do 8 and 4, so his active service ended in 06. He then started his 4 years Section B Reserve service (ie home in his civilian job but committed to recall). He received a little daily pay and he had to do one day's training a year. After the 4 years were up in 1910 he signed on for 4 more years on what was termed Section D Reserve, similiar terms to Section B. A way of getting a little monthly to help keep the family. Then the war broke out and as a reservist he would have been mobilised in August 1914. He was found not physically fit for war service in October 1914.
With the clasps as a basis, anything you can find to read about the Royal Engineers in South Africa will help add more to the story.
The medal rolls are on Ancestry if you have access? If not I can direct you to the right place at the National Archives where the rolls can be downloaded free.
MaxD