Graham. As far as I know, the dedicated support vehicles are commonly known by their GRAU code (which greatly facilitates the search).
“Standardization” of Russian equipment is not so obvious but the mechanics in Russian army seems to have organized this m**s in their own organization. In the case of MTP wrecker, codes -A1, -A1.2, and -A2 means respectively that the vehicle is an Ural-375D, an Ural-4320 or in this case, a KamAZ-43114
I know that МТП-А2 is part of ПАРМ-1АМ1, trucks-dedicated mobile repair shop which includes workshops, lifting equipment and trailers.
To troubleshoot or maintain units with specific ГМ-*** vehicles like Tunguska, it is the ПАРМ-1АГ3М repair shop variant, but I have not search its composition.
Maybe our friend Glorfindel who like TO&E will be able to help us. By the way, are there Russian dudes on the Forum?