In Ballistol, the mineral oil is merely the base. I used to have a listing of the formula and it had a lot of ingredients besides mineral oil. The MDS sheet doesn't list all the ingredients, whereas the patent does, if you can find it.
I know it has cetyl alcohol as an emulsifying agent. I remember several solvent sounding names such as octyl something or other. It also has several botanical oils, anise oil being one of them.
Remember it's original design called for it being antiseptic also. It also combines with the leftover acids from the tanning process in leather to form a waterproof compound. These might be clues as to what else it contains.
Sometimes blends like that aren't merely mixed together, but are reacted under heat and/or pressure to get the components to form new compounds. I don't think it would be easy to mix up a batch yourself.
Paul is right about mixing it with water, soaking the patches and letting them dry. I use a ratio of 1 part Ballistol to 5-7 parts water, depending on the gun. They each have their favorite ratio. When the water evaporates out, it leaves the patch evenly and lightly lubed. Something that is impossible to achieve using straight Ballistol.
You could probably lube up a bunch of patches with mineral oil and press out the excess to achieve something similar, if you want to test pure mineral oil as a patch lube.