This cleaner works because the turpentine or mineral spirits dissolves wax, grease, and residue from fingerprints, as well as those small paint flecks from repainting a room with a roller. The linseed oil restores some color to the wood and appears to revive the existing finish. 0000 steel wood is the finest grade, so it cleans without scratching.
Here are Before and After photos of a neglected walnut stock from a U.S. 1898 Krag carbine. As found, before cleaning:
Some original finish can be seen, but it's gone from most of the stock. Water has stained the butt end,and, unfortunately, this cleaner can do nothing about that.
After cleaning with the linseed oil and mineral spirits applied with 0000 steel wool:
Obviously, the cleaning has evened out the color of the stock. Perhaps that should be qualified: evened out the color of the wood--if you look closely an inch or so away from the butt plate, you can see lighter spots where someone filled some holes with plastic wood. But now the stock no longer looks neglected.
Some notes on use: Boiled linseed oil, not raw.
Linseed oil can spontaneously combust, so dispose of the steel wool and rags carefully. I wet them with water and then put them in a plastic bag.
Don't slop it on: the mixture can stain upholstery or your clothes or carpeting.
Don't take this mixture internally: it's bad for your health.
Use the steel wool with a light touch: you're not trying to get down to bare wood but to clean the finish. Two light goings-over are far better than one heavy-handed one.
Don't skip the twenty-four hours later wipe-down. If you missed some areas, the mineral spirits will evaporate, but the linseed oil will remain sticky and collect dust before it dries.
If you want to wax the piece, wait until you can't smell the linseed oil any more.
Finally, three "If's": If the wood is antique cherry, test on an area you can't see. Some old cherry was stained but never given a finish coat, and this mix can dissolve the stain. If you're not sure what the wood is, test it where you can't see it.
If you have a funky painted piece with the paint going chalky, don't mess with it. That patinated surface is part of its interest. As John T. Kirk has commented in his excellent Impecunious Collector's Guide to American Antiques, "buy it ratty and leave it alone."
If the piece of furniture (or gun) is museum quality, don't touch it. I've read statements by curators saying that this mix will blacken wood. I've used this mix for fifty years on walnut and mahogany and haven't seen that happen. But don't gamble: get in touch with a local museum and ask for guidance. The museum people will bless you for it.