I hope Jake will forgive me for jumping in with an answer to this one; I'm nursing a case of sunburn-induced insomnia at 5:30 a.m., looking for something to type about.
James Lees's The Masting and Rigging of English Ships of War, 1625-1860 gives 1811 for the introduction of jackstays. He, of course, is talking strictly about British warships, but I think that date is about right for other nations - and for the merchant service - as well. Like all other developments in maritime technology, of course, this one was gradual; not all ships got jackstays at the same time - and some never got them.
In its initial form the jackstay consisted of a piece of rope running through a series of iron eyebolts driven, at intervals of about three feet, into the top of the yard. I've read that jackstays sometimes were made out of wood, though I'm having trouble thinking of a specific set of plans with wood jackstays on them. Sometime in the mid-nineteenth century the iron jackstay came into use. It was essentially like the old rope version, except that the rope running through the eyes was now a piece of iron rod. I'm not sure when the first iron jackstay appeared, but it certainly was in common use by the middle of the nineteenth century. The classic American and British packet ships, clipper ships, and whalers seem, in general, to have had iron jackstays.
The jackstay had two functions. First, it served as a place to fasten various pieces of gear that, in earlier periods, had been secured to the yard itself. The robands (the lines that secured the head of the sail), the footrope stirrups, and various other gear (such as the buntline and leechline blocks) all came to be lashed to the jackstay. Sailors quickly figured out that the jackstay was useful for another purpose: it made a convenient thing to hang onto.
Eventually (I don't know exactly when, but probably around the turn of the twentieth century) it occurred to somebody that things would be more orderly if the the various functions of the jackstay were divided. The big steel ships and barques of the last days of sail often (by no means always) had double jackstays. One remained on top of the yard; the second jackstay was mounted 45 degrees forward of it. The head of the sail was secured to the forward jackstay; the other pieces of gear remained on the upper one (which the sailors also used for a handhold).
Plastic kit manufacturers have dealt with jackstays in several ways. The grand old Revell 1/96 kits of the fifties and sixties, the Cutty Sark and Kearsarge (along with their dubious clones, the Thermopylae, Pedro Nunes, and Alabama) had tiny pins molded on tops of the yards to represent the jackstay eyebolts. (The big Revell Constitution doesn't have them. It seems to be generally agreed that the Constitution didn't get jackstays till well after the War of 1812.) It's relatively easy to glue pieces of wire to the pins to represent the jackstays themselves. (The instructions in the first few issues of the Cutty Sark told the modeler to do that - and to buy 12 feet of 36-link chain to represent parts of the running rigging.)
Some of the smaller Revell kits (including, I think, the 1/192 Constitution) had jackstays, in the form of a narrow ridge with little bumps on it, molded integrally with their yards. I think Aurora did the same thing with a couple of its kits; I'm not sure whether Airfix did or not. Actually, on such a small scale that probably wasn't such a bad idea. On a real ship the jackstay is separated from the yard by an inch or two; on any scale smaller than 1/96 that's pretty hard to represent realistically.
I only remember two Heller kits that tried to represent jackstays: the Pamir and Passat. (I imagine the Preussen did too, but I never bought it.) Here, as in so many other instances, the Heller designers combined great skill and ingenuity with an utter failure to understand the prototype. They molded a series of little rectangular blocks on each yard to represent the jackstay eyebolts, and advised the modeler to glue pieces of wire or thread to them. Not such a bad idea - but they put the "eyebolts" on the fronts of the yards. That's ridiculous.
Making your own jackstays, with no help from the manufacturer, isn't easy. It entails drilling a series of small holes in the yard, all in a precisely straight line. Scratchbuilders sometimes tackle the problem by drilling the holes in some sort of jig, before the yard gets tapered. It's occurred to me that a set of generic jackstays on various scales would be a good product for some enterprising photo-etching firm. Maybe every fifth or sixth "eyebolt" could have a long shank to go into a hole in the yard, while the others were cut short and glued to the surface with no holes. Maybe it wouldn't work, but it might be worth a try.
Too long as usual - but the subject is interesting. I'm going back to bed.