In my universe the TMM was created using equipment of the Tamar Jagers and planetary militias. Why?
The Jagers are units that were mentioned in early sourcebooks, but nowwhere later. We haven't seen any hint what happened to them.
We know they had once 4 mechs of mostly medium mechs (even, when the camospecs booklet shows us a Zeus - maybe thats what is called a lyran medium). We know they were somehwere between green and regular. And we know from TRO3026 that they took heavy losses on Memmingen.
In my eyes it sounds valid that with the reorganization of the Armed Forces of the Federated Commonwealth in 3041 units like the Tamar Jagers, maybe seen as private army of an unloved march lord, was reorganized too. Using the reminders of the 4 regiments and using local militia to build up 6 new TMM regiments.
That said in my universe the TMM used a variation of red and black to honor the heritage of the Tamar Pact.