larryc,
I have recently being looking at Williiam as part of my research into recipients of the Wepener clasp. My records show he received QSA (5) CC Wep Tr Witt SA01. I do not have any information beyond what you have written.
Most of the regimental records that I have seen suggest that the units were disbanded very quickly after peace was signed. It is usual to see people's service coming to an end in June 1902 on disbandment of their unit. I was working on the Driscoll's Scout roll last night and that unit was disbanded on 30 June 1902.
It would be unusual to see units going on beyond July but there may be reasons why Burghersdorp DMT continued. The impetus from London would have been to disband the local units as quickly as possible to save the money.
As a DMT, I think the members would have a lot more freedom of movement compared to an Imperial unit and that permission to travel would have been easier to obtain once the war ended.
These are just my speculations on what might have happened.
Kind regards
David