There is also what was termed the 'Section Cleaning Kit". These usually ended up with a member of the machine-gun group. This had a multi-section steel rod, brushes / jags and a ruptured-case extractor. For the keen, the NSN for the cover, at least, is; 1005-66-100-2017.
This, in turn, is not to be confused with the Australiancleaning kit for the M-60 GPMG. Whilst being a similar "tool-roll" design, with rod sections, bore brushes, etc., it also had a (or SHOULD have had), a nifty brush for cleaning inside of the body. This had a mix of stainless-steel and nylon bristles and was SQUARE in cross-section, to better clean out the various "channels" in the receiver body. There are a couple of "used / pre-loved" ones in the "random cleaning stuff" box, as I don't own an M-60, nor could I afford to run one if I did.