Note a few things. First off, the finish on the guitar isn't varnish. Most modern are considered 'poly' which is either a polyester resin or polyurethane. OLD guitars (before the mid to late 60's mostly had nitrocellulose lacquer, or 'nitro', which aged more quickly and was a more delicate finish.
As a long time furniture maker and professionally trained finisher, I have to chime in.
Polyurethane most certainly is a "varnish", just with a specific resin. Old school varnishes used phenolic resins, then there are urethanes, and then polyurethanes. They're all varnishes, some are oil based, others are water "based", but are actually glycols that can be thinned or cleaned up with water. All of these products molecularily crosslink as they cure, they don't dry. Applying the solvent to a cured finish won't redissolve it.
In Europe, shellac is often referred to as "spirit varnish" as it's alcohol based. Shellac redissolves if alcohol is applied, even many decades later, as it doesn't crosslink. This is known as an evaporative finish, because it doesn't cure, it "dries" as the alchohol evaporates.
Lacquer is simply a plastic or cotton based resin dissolved in a solvent. It is also non-crosslinking and will be redissolved by it's own solvent forever.
Lacquer and shellac resins are harder and far less flexible than urethanes or phenolic resins. This makes the two easier to buff up or down to a variable shine, but far more likely to crack, chip or alligator.
All are known as varnishes in different circles...
The crosslinking feature of phenolic and urethane resins makes them stay slightly softer and flexible, making them more durable and less likely to crack, but nearly impossible to repair and harder to buff. The redissolvable feature of lacquer and shellac make them easy to repair and subsequent coats melt the previous or "burn in". If a crosslinked finish is rubbed out, it often develops white lines that look like a topo map, known as witness lines, as you rub through different coats.
A big part of the yellowing that happens to certain finishes is actually a function of the oils (linseed, tung, etc...) used in the base aging. It's why waterbourne and alcohol based finishes stay water clear so much longer than petroleum based versions, and are often chosen for very light woods where "ambering" is not desired. The ambering process enhances darker woods, so amber dye is often added to non-ambering finishes.
Dyes are often added to age a new finish on vintage reproductions.
Hope this is useful!