Howard's is a short term make do treatment at best. It's basically mineral oil, plus mineral spirits and other solvents, including isopropal alcohol, acetone, with small amounts of toluene and xylene. In some versions color comes from Gilsonite, which is essentially roof tar.
The more volatile of the solvents evaporate pretty quickly. The mineral oil (paraffin oil) stays around a little longer. It does NOT cure or dry. If enough is applied to leave the surface a bit wet, it just collects dirt.
The oil offers virtually no protection to the surface and won't protect from water damage. Application does often cure white rings--that's due to the alcohol penetrating the existing finish and bonding with water vapor that is causing the ring and helping it evaporate away. A few light passes of alcohol by itself would do the same thing.
There are much more permanent treatments available. I would clean surfaces with water, with just a couple of drops of "Dawn" to break the surface tension, then I would use naphtha (mineral spirit) to wipe off oily dirt, using a copious supply of paper towels so the dirt is removed not just smeared around. If the finish is a matt "oil finish" that doesn't have a film on the surface you can freshen it up with a mix of oil and varnish, such as Watco. Finishes that are suface films typically need to be stripped off with chemical stripper. Don't try to sand it off--sanding doesn't leave a very evenly prepared surface, AND since the surface is typically veneer, it is way to easy to sand through the veneer. If that happens the fix is either expensive or not very satisfactory.
