I have always assumed that the clues to the TG's and DMT's lay in their names. The TG's were just that, dismounted men who patrolled the towns, whereas the DMT's took care of defence in the countryside surrounding towns and therefore had to be mounted.
Another assumption was that the DMT's of the Cape Colony were called Rifle Associations in Natal.
Some time ago, I chanced upon a CD containing the blank attestation forms to be filled out by Colonial chaps upon enlistment. I can't help myself with that sort of stuff! Anyway, the forms for would-be DMT enlistees were those provided for in the Colonial Defence Force under the Order 32 of 17/8/1901.
The regulations are interesting in that the size of the total size of the DMTs is defined - and the area of service a DMT s was engaged to serve inside was their own district.. TGs were engaged to serve only in the immediate vicinity of their own towns. Both were classified as Class C units.There is a lot more info possibly of interest; however my printed put out pretty crook copies of the relevant pages. I will have a go at taking pics and see it that gives more readable copy. At the moment, I have to read the printed out pages with a magnifying glass