Do CEDAR TOPS Darken with Age?

There's a fair range in the color of cedar, so part of the difference is just the wood that was chosen (also, many classical guitars have spruce tops... so be sure you're comparing apples to apples!)

The wood itself isn't going to darken - it's been aged for years before it was turned into a guitar, so the way it looks is pretty much the way the wood will stay. The finish is another story...

High-end classical guitars are traditionally finished with 'french polish', a technique that dissolves a shellac or other gum in a medium that will mostly evaporate, like turpentine. These finishes are soft, and over the years they will develop a 'patina' that's a combination of the yellowing of the gum and the inclusion of specs of dirt, cigarette smoke, whatever it's been exposed to.

Other finishes, like lacquers, aren't so permeable to dirt... but the finish itself is usually a plastic base that will yellow eventually. If an instrument is more than 70 years old, it's almost certainly a french-polish; if it's less than that, it's likely French polish if it's expensive, and lacquer if it's not - either way, the finish will darken over time.

The wood itself isn't going to darken - it's been aged for years before it was turned into a guitar, so the way it looks is pretty much the way the wood will stay

Sorry to disagree, but the wood WILL darken. Aging takes place out of direct sunlight - in the early years of maturing, direct sunlight will cause uneven warming of the wood and consequent splitting. There will be little or no change from it's colour as "green" wood.

However, long exposure to sunlight will cause discolouration

You can do a simple test. Take a cheap piece of untreated wood and cover part of it with a book. Leave it on a windowsill, in direct sunlight, over summer. If you take the book away, you will see a faint difference in colour, which will increase with the length of time that the wood remains on the windowsill, partially covered by the book.

This is also the reason that a newspaper will turn brown oveer a period of years - the wood pulp is discolouring - the process is accelerated by acids used in the paper making process.