I have been using SHEATH since around 1963, and the way I use it is the same as you did-I saturaste a cleaning patch (2.5'X2.5 square GI patch) with the stuff, then use it to swab the bore about four passes with a jag on a cleaning rod, just like you do with the solvent when cleaning.

I then use the same patch to wipe all the exterior metal surfaces. From your description, I think I do it the same way you did. It works that way!

(Back when I started using this stuff, it came in a can with a plastic spout, just like 3-in-1 Oil. It was not in a spray can, like it is now. So now I just spray the patch until it is good & wet with the SHEATH......)