I only do the tops of some of my instruments with the Tried and True or Naturhaus. The back and sides, neck etc I French polish or Varnish. But then I make 19th century guitar copies from about a dozen different makers so generally I try to copy what the original maker did. Some of the makers used French Polish, some wax and/or oil and some oil varnish.
How you do the back and sides depends a bit on if you fill the pores in the wood or not and persomal choice. I use a mixture of eggwhite, pumis and sanding dust to fill the pores before French Polish or varnish. This gives you a glass smooth surface to start with. Others like the look of natural wood pores so it's up to you. I've never really tried the eggwhite filler under oil as I don't fill my tops. I don't think the oil would lift the filler but I'd try it on a scrap piece before just to check it out if one were to go that route.
You can skip that filler step if using French Polish or varnish and you build up the finish enough to level it again to the surface of the pores. I don't like this method as it wastes a lot of finish and is just more work. The finish shrinks over time so I find I always end up with pores showing anyways if I go this route. That's why I fill first.
I personally have not used any of the oils mentioned on the whole instrument but have seen a few done that way. I think it's fine but just not my choice. I like the look of a beautiful figured Maple or Rosewood or what have you as it shines under a finely applied French Polish or Varnish.
One thing I've not figured out satisfactually is how to stop the dirty look that comes to the high contact areas of an oiled finish (ie. the area where ones right arm touches the instrument top, pinky finger marks if one plants that finger on the top etc.). The Naturhaus with the Hard Wax finish is much better than the others I've tried but one has to reapply the wax every so often and performers tend to neglect keeping the routine up. One still gets marks in those areas with Shellac/French Polish anyways, so maybe it's just a fact of life in the end.
With the varnish Oil you can get a pretty high gloss finish, not as high as Shellac or Varnish mind you, if you apply enough coats and burnish the heck out of it (I've gone as high as 20+ to see how far I could go before getting sick of applying oil) .
No metal driers in Tru Oil (according to the MSDS) although it does contain mineral turpentine.
The Varnish Oil contains a 'high resin content' which indicates that it will eventually build into a gloss finish - if that is what is desired. No doubt that you could also use it on the soundboard as well, although it will probably give a finish somewhere between matte and gloss providing you limit the number of coats. They clearly state that it contains no solvents. Polymerised oil with a high resin content, yet is a wipe on finish - don't quite know how they manage that but I guess it must work.
This addition to the replies may be irrelevant but as Akira now has one of my guitars made more than thirty years ago and apparently 'as new',I should say that at that time I was using a commercial spirit varnish, available only in 'clear' and 'brown'. Of course I cannot now remember the name! And I believe that it is no longer available. It was basically a resin + alcohol mixture, reasonably hard-wearing, and I always put as few coats as possible on soundboards. It dried very fast, but new coats tended to soften previous coats, making it very difficult to use the coloured varnish. It certainly tended to take away the upper partials from notes although I find that they have come back on another thirty-year old instrument, a lute, that I know still.
I'm now using home-made oil varnishes but 'unvarnished' soundboards are problematical. My own solution does not keep them clean or really washable, but does prevent grease from fingers soaking in and damping the sound. It may even be authentic! I use a size made from dilute glue (about 6 X water added to working animal glue) This is used all over my instruments. The soundboard areas have alum added to the size - up to an amount approximately equal to the original glue before adding water. Keen photographers will know that alum is the hardener used with gelatin negatives. If there is any danger, or even just fear, of warm size re-melting the glue used in construction, it can be allowed to set to a soft jelly and rubbed on with foam plastic, sponge, cloth etc. Probably two coats with gentle sanding between because the grain will be raised. No alum under the varnish because it can sometimes form tiny crystals which will spoil the finish, but can be merely rubbed off on a soundboard. Alum works by raising the melting point of the glue leaving a thin hard protective layer.
Sun-thickened oils, stand-oil especially, were used by artists because they yellowed less than ordinary linseed oil. However for instrument soundboards generally they will add weight by firstly soaking into the wood and secondly by their oxidising drying process which will add even more weight. This latter may be desirable for violin sound, but violins have one or more 'size' layers below the varnish to prevent its soaking into the wood. Bear in mind also that most woods change colour with time and light.
Another possibility which makers could experiment with and which I have used on 'non-authentic' instruments where a matt finish was desirable is to rub the instrument over with plenty of white spirit/turps subs, followed immediately with a second rub over with a polyurethane varnish diluted with about twice its volume of white spirit. The first coat prevents the varnish from soaking-in. I have used Ronseal gloss, dried overnight, almost always not requiring a second coat, especially on simple shapes like dulcimers, etc. Use a clean cloth and dispose of it safely. Again the result is a thin hard surface layer.