According to his obituary, he was 15 while in Ladysmith, so did he join the Town Guard or any other military unit?
"Major King, who was 55 and was born in South Africa, was in the siege of Ladysmith when 15, and took part in the Great War, being badly gassed at Poperinghe, and later was training men for the front. [.....] He was a [....] member of the British Legion and South African War Veterans of Chudlegh and district." Devon and Exeter Gazette, 1st September 1939
I had a look in "The Ladysmith Siege" by G.W.Lines (a contemporary booklet, reprinted by the NMP). G.W.Lines was Secretary and Treasurer of the Ladysmith TG. There is no entry for a J.King for any of the various Wards, etc, comprising the TG. Nor in the list of town residents (I do not know how definitive that is). I tried to have a look on WO100/283 - but could not get a response.
At fifteen years of age, a bit young for the TG - perhaps a "runner" for them?