RootsChat.Com

South African Archives has a service record for him

DEPOT     TAB                                                                   
SOURCE    SAC                                                                   
TYPE      LEER                                                                 
VOLUME_NO 66                                                                   
SYSTEM    01                                                                   
REFERENCE B1006                                                                 
PART      1                                                                     
DESCRIPTION          RECORD OF CONDUCT AND SERVICE OF SOUTH AFRICAN CONSTABULARY EDGAR     
           ETCHES.                                                             
STARTING  1900                                                                 
ENDING    1905                                                                 

The following Hesom men served with Natal Carbineers.  Taken fromt he records at the NC Museum

HESOM George Plummer Cyril.  Trooper E3653
Attested:  1/7/1916, A Sqn.  Age : 18.  Occupation: 341 Bulwer Street, Pietermaritzburg.  Promoted Lance Sergeant 1/1/1922 (RO 37/1922) and Sergeant 1/8/1923(RO 1/8/1923).  Off strength:  30/6/1925
Other:  Completed Instructors Vickers Gun Course at S.A. Military School 10/2/1922 (RO 42/1922)

HESOM G.T.F.  Trooper K4986
Attested:  3/10/1918, A Sqn.  Occupation: 310 Boom Street, Pietermaritzburg.  Off strength:  31/12/1919


HESOM N.F. 273
On strength 25/11/1893.  From Dundee.   

HESOM Owen.  Trooper 584. 
Attested 12/2/1899, K sqn.   Occupation : Farmer, Dundee.  Siege of Ladysmith.   Served 29/9/1899 to 31/5/1902.  Off strength 30/6/1903

HESOM Robert.   Trooper 255. 
Born 13 October 1873, Dundee.  Son of George Thomas Hesom, Husband of Ida Bowen.  Educated at Maritzburg College.  Attested 19/7/1893, Band.  Occupation : Manager, George and Son, 313 Prince Alfred St., Pietermaritzburg.   Won first prize for the smartest turnout with the NC in 1896.  Awarded Queens Jubilee Medal 1897.  Promoted Corporal 29/4/1897.  Siege of Ladysmith.  Served 29/9/1899 to 31/5/1902.  Promoted Lance Sergeant 10/5/1903.  Off strength 31/3/1905.  Previous service with 2nd ILH 31/8/1901-30/11/1901

I think it is the Tongaat troop.  The Fynney family had a sugar estate in Tongaat.  It would possilbe have been one of the mounted rifle troops

Try this site

http://www.angloboerwar.com/south-african-units/350-kitcheners-fighting-scouts