Additional side notes... Vinegar does remove rust, but it also normally requires the item in question to be submerged and soaked for a certain degree of time for it to do its work. Gun barrels tend to be problematic unless you have a suitable trough to put it in. A simple rub down with it usually doesnt do much. However vinegar will also start to eat the base metal if left in it too long. I run an antique and restoration business, so have a wide variety of different methods to remove rust, corrosion, grime depending on what the metal is, severity of corrosion as well as what the desired end result is being sought after. Depending on what Im working on I frequently make use of Citric Acid, Oxalic Acid, Electrolysis or Ultrasonic tank dunking, amongst others. Of course there are other corrosion eaters out there thats cheaper and more readily available that others use such as Vinegar, Molasses or Lye baths.. Each has their own pro's and con's to be aware of.
Ahh.. now see the pics uploaded.. If it were me I would be inclinded use the oil/steel wool. Another option in this case since the rust only appears to be superficial on the surface. There is a cleaning product called "Bar Keepers Friend"... comes in both a powder and a liquid form. Its a micro grit cleaner marketed for metalwork and countertops, however it also contains Oxalic Acid that does very well in handling and disolving minor rust issues. It also does great on brass, bronze, copper as well without turning it pink. Used with an old tooth brush in a circular motion works well. You can also see the effects its doing as you go along so less likely to accidently take it too far than you want too. (We use the same stuff on our bronze 12lb Napoleon when we want a good shine on her... however not with a toothbrush in this case!)..