I was mistaken in saying the roll WO 126/146 Town Guards and District Mounted Troops was not online, it is within those listed on http://angloboerwar.com/unit-information/south-african-units...
; no papers for anyone named Beech/Beach.
When notes appear against the crossed out names in entries in QSA medal rolls, they state a number of reasons, including men who, deserted, or they are listed in another roll for troops they were on detachment with, and in the case of some Town Guards, men who never any action (actually noted) on some town guard rolls, but as I said previously the R Beech in the King William's Town Guard had no such notes and he wasn't the only one in that Roll.
Assuming the person you seek served with another SA raised unit, can I suggest, that where there are enrollment forms or a nominal roll on linked pages, you do a name check for each of the units mentioned at http://angloboerwar.com/unit-information/south-african-units
Note that for some units if nothing is shown when you click on a unit title, click the next button.