Stan, a while back I was curious about this subject and went down the internet rabbit hole looking for the same answers you are.
I found dozens of claims that sunlight degrades case hardening colors over time. And I also found many people saying that sunlight has no effect whatsoever. However, I found no credible tests to determine if the claims of fading due to sunlight have any basis in fact. Naturally, I checked Doug Turnbull's website to see if he had any insights, and he didn't address it there. So it was interesting to see Ted say Turnbull does have an opinion. I did find some guys who claim they do bone charcoal case hardening that did say sunlight may fade the colors over time, but none of them showed any proof. I'm not sure how valid testing could be done since samples exposed to weather would oxidize, and window glass filters out a lot of UV light.
Since then, I concluded that this claim is probably just another myth that became accepted as fact after being repeated so many times... something like the myths that all Damascus barrels are dangerous to shoot, shiny bores on vintage shotguns means probable honing, or that small bore Ithaca Flues frames are especially prone to cracking.
On the other hand, if the colors we see are at least partially the product of the formation of some iron oxides frozen during the quench into the top couple thousandths of the surface, I could maybe accept that prolonged exposure to very direct sunlight might have at least a minor effect on those colors over time. I say that only because we know that metallic oxides have long been used as pigments for oil paints, stains, and dyes for cloth. All of those things do seem to be subject to fading from sunlight. However, they are not part of the crystalline molecular structure of the surfaces they are applied to as case hardening colors are. For that reason, I have never worried about using my guns with strong case colors on sunny days, and have never worried that I should be covering them with lacquer or anything but the same gun oils I use to protect the blue on my barrels. I avoid wax on case colors because many waxes contain mild abrasives. And I've also assumed that the old guns I have with faded or nearly non-existent case colors got that way because previous owners just didn't care for them properly. I'd be much more concerned about not cleaning and oiling my guns after exposure to rain, snow, perspiration, or even handling case colored surfaces with leather gloves impregnated with abrasive dust or tanning chemicals.
