You said, "I know he was reported as "missing in action" very early on"
I searched the Times digital archives for a report of him being missing but the only mention of him that I could find was:
The Times, Tuesday, Mar 20, 1900; pg. 7; Issue 36094
Casualties.
Part way through the report was:
The following further deaths are reported from Cape Town:-
List includes 6611 Pte H. Thomson, 1st Argyll and Sutherland Highlanders, enteric, Kimberley, March 15.
Although that appears to be slightly at odds with his service end date you quoted of 13 Feb 1900, such small differences were common.
The remarks column of the QSA Medal Roll notes “deceased”, so no service record will survive for him.
Although he's listed in the "Casualties of the Boer War" as died, it was taken from a published version of casualty report. To be certain there are no additional notes or amendments, you need to see an actual copy of
WO 108/338 “List of Casualties in the South African Field Force from 11 October 1899 to 20 March 1900”
It’s one of several volumes of casualties held at the National Archives, Kew, but has not been digitised. I have only got an extract, unfortunately it doesn’t cover the Argylls; if he was officially posted missing he will be listed.
If you cannot get to Kew, the only way I can suggest you obtain more details about him being reported missing is to contact the Regiment’s archives, but there’s a minimum fee of £25 see
http://www.argylls.co.uk/research/