Jim,
The vinegar in the mixture of rotten-stone and vinegar is to make the rotten-stone a slurry that can be pushed around with a cloth pad. It is not intended to contribute to the rusting process as it is not left on the gun part like the browning solution is. But in chemistry we are taught that like dissolves like. Meaning that if you want to dissolve the product of an acid use an acidic solvent. vinegar is a solution of acetic acid, a mild acid compared to the nitric acid in the browning solution.
Browning is a process where the iron substrate is covered with a layer of iron oxide - a mixture of ferric oxide and ferrosoferic oxide. If you use a strong reagent and long application times the reagent will form pits in the surface of the steel. The pit will be filled with iron oxides. Under a microscope the pits will look like freckles. The repetitive application of reagent causes more and more freckles to form until they cover the entire surface of the steel with freckles and any area between freckles is filled with another freckle. This makes an inherently rough surface if the pits are deep. Deep pits come from long application times. Deep pits are facilitated with a rough beginning surface. If you polish to 200 grit and apply your first dose or reagent, after a few hours microscopic inspection will show you a sting of roughly elongated pits along each scratch. If you use a mild reagent, on a finely polished surface, with short application times, followed by a very fine abrasive you can achieve a glassy brown finish. It is a time-consuming, laborious process but can yield beautiful results.
That's all I know.
Best Regards,
JMC
John Cholin