The whole subject of rigging color is an interesting one. I don't think there's a straight answer to Don's question.
Modern, operating ships aren't of much help. They almost invariably have synthetic rigging, which comes in colors.
All we really have to go on are paintings and old photos. Both are pretty ambiguous. The old masters generally seem to have used dark brown for almost all rigging, and the photos invariably are in black and white.
The only real documentation I've seen deal with the British Navy in the seventeenth, eighteenth, and early nineteenth centuries. During that period all line supplied to the Royal Navy was legally required to be soaked in Stockholm tar. It has a rich, medium brown color. There are lots of references to "blackening" the standing rigging with a mixture of tar, sulfur, and lampblack, which, if it wasn't pure black, must have been pretty close.
Whether the deadeye lanyards got "blackened" or not I don't know. But tar wouldn't make the rope rigid. In the aforementioned paintings and photos I can't recall ever noting an obvious distinction in color between the shrouds and the lanyards. I think this is another place where individual judgment and taste rule the day.
For what it's worth, the deadeye lanyards of the recently restored Charles W. Morgan are black. I have no idea what sort of rope was used, but the restorers at Mystic Seaport are among the best in the business. I'm sure they had good reasons for rigging her the way they did.
One general observation. Many model builders, for some reason, make their running rigging too light in color. Sometimes white. I think one reason is that wood kit manufacturers sometimes supply white line with their kits. Nowadays many boats and ships are rigged with white synthetic line, but of course no such stuff existed until a few decades ago. ( I was really bugged by the ship in the 1983 movie "The Bounty." All the running rigging was pure white.) The running rigging of a real, pre-twentieth-century sailing ship would have ranged in color from dull tan to medium brown - because it was natural fiber rope. (Those nice running rigging lines in the photo above won't stay that color for long - unless they're synthetic.)
Caveat: photos of models can be deceptive - especially flash photos. More than once I've deleted pictures of my models because the running rigging literally lit up under bright lights. Don't assume the rigging is too light on the sole basis of photos.
At just about the middle of the nineteenth century, rigging started to be made of wire. Some of the Cutty Sark's standing rigging is wire. (The George Campbell plans specify which lines.) The wire was made of iron (or later steel). It frequently was coated with tar (as a rustproofer), so it wouldn't look much different than rope standing rigging. If I remember correctly, the pendants for the Cutty Sark's braces are wire. By the beginning of the twentieth century - the time of the big German steel barks - wire had virtually taken over for standing rigging.
I've said it before and I'll say it again: I wish somebody would do a really thorough, scholarly study of the colors of rigging line over the centuries - and, for that matter, in different countries.
Until that happens, I'll repeat the two Golden Rules for ship model rigging: One - if in doubt as to size, err on the small size. Two (with apologies to Darth Vader): if in doubt as to color, err on the dark side.
Happy Thanksgiving, everybody!