I've been trying to sort out the question of rigging line colors for close to fifty years now. My final, definitive answer, based on studying documents, photographs, paintings, models, and real ships is (drum roll please).....I don't know.
This subject doesn't seem to be at all well documented. The only firm reference I've seen to rigging color is the British eighteenth-century law requiring that all rope supplied to the Royal Navy be soaked in Stockholm tar. I don't think I've ever seen Stockholm tar, but as I understand it its color is a warm medium brown. That would seem to be the appropriate color for running rigging on eighteenth- and early-nineteenth-century British warships. That's about as far as I feel comfortable going.
I have the strong impression that the practice of coating the standing rigging with tar after the rigging was set up was common at least as early as the mid-seventeenth century (but I'm not sure about that date range). The "tar" in question apparently was a nasty mixture of tar, lampblack, and other stuff that, if it wasn't pure black, must have been pretty close.
Sources on rigging colors can be really deceptive. Photographs of the real ships are almost useless; they almost invariably show the rigging in silhouette. The works of the great marine painters have the same problem. Restored sailing ships and replicas almost always are rigged with modern synthetics. (They have to be, in order to be economically viable.)
The vast majority of contemporary ship models from the seventeeth, eighteenth, and nineteenteenth centuries have been rerigged in the twentieth (or twenty-first) century. (Most of the magnificent models in the Rodgers Collection at Annapolis, for instance, were rigged by Henry Culver in the 1920s and '30s.) The few old models that still have their original rigging have been around so long that the color of it is almost irrelevant. I've worked on several nineteenth-century models whose rigging had been coated with varnish, which makes the thread considerably darker than it presumably was originality.
I don't have a real answer to the question of tarring deadeye lanyards and ratlines, either. I've seen conflicting evidence in paintings and models. Some people have gotten rather emotional about the subject of tarred ratlines. Those people's strong opinions not withstanding, I don't think there's a universal answer to that one either.
One point: it seems to me that, though a shroud could certainly be set up and tarred before the ratlines were added, it would be mighty difficult (and time-consuming) to recoat the shroud with tar after the ratlines were in place. (The ratlines would almost have to be removed until the job was done. That seems highly unlikely.) And records indicate that "re-blackening" the standing rigging was quite a common practice.
I will repeat what I regard as the two golden rules of ship model rigging: 1. If in doubt as to diameter, err on the small side. 2. If in doubt as to color, err on the dark side. (I can't understand why modelers make standing rigging out of white thread.)
My personal answer to the basic question: I don't know. And I frankly question whether anybody else does.