I've gathered here numerous period photos of sontags and maybe-sontags, and some not-quite-sontags, as part of my research as I knit one for myself. I remember some historical costumers sighing over the fact that all of the sontags they saw at re-enactments were knitted to the same pattern, again and again, but it's pretty obvious from these photographs that there must have been as many different versions as there were knitters, so that unless the modern knitter is actually re-creating a period pattern, there is no reason why you need to stick to the basketweave one from Godey's.
The version worn by the lady above might be knitted in a honeycomb stitch, to which she has added a two-color crochet edging. She also appears to be wearing fluffy netted sleeves.
Here are three original patterns --
the earliest one from the 1860 Godey's,
another one from the next year's Godey's (1861), (A "habit-shirt" was a sort of dickey, or as Chambers' dictionary has it, "a thin muslin or lace under-garment worn by women on the neck and shoulders, under the dress", which sort of makes sense but not quite here, as of course the sontag is worn over one's dress.)
and a third by Mrs. Weaver, in Peterson's Magazine of 1862. The two Godey's patterns are very similar in effect, especially with the faux ermine trim (!), but the first one will result in a definite U-shaped piece, while the second will give you a V-shaped piece, since you not only start with only five sts but you also don't cast off any sts at the back neck. There is no mention at all in the second one of closures, whether ties or button.
Mrs. Weaver's is different yet again, as while she does use the U-shape (which would certainly sit better on the wearer's neck), her front points appear to be a little squared off, and at least in the illustration don't wrap around the wearer's body. She is unfortunately rather non-committal about how one secures it, which might explain the solution of these two ladies --
The photographer has with his highlighting unfortunately obscured the details of this lady's sontag, but it has a very similar crocheted border to that of the lady in the top photograph, though here the shell stitch is in a single color.
This one appears to be entirely crocheted, but is not perhaps strictly a sontag either, since the ends don't seem to go all of the way around the wearer's waist and attach to the back of the garment.
This lady's sontag has a deeper and frillier border than most, which make it come further down the upper arm than the previous ones. Her ties are also longer than the others, but also end in pom-poms.
This lady has chosen a very striking three-toned stripe for her sontag. It's too bad that her arms are in the way, as it looks like the points of the sontag end in the front, presumably with ties that wrap all of the way around and back to the front.
This is I think the most "famous" example of a sontag now, as it's the one you see most often if you Google "sontag bosom friend". It appears to be entirely crocheted, and unlike the 1860 Godey's pattern, has ties that wrap all of the way around and back to the front.
This lady's is quite vivid with its checked two-color pattern!
This is the only one I have seen that does not have a contrasting border. It's too bad the image isn't bigger, as it looks like she might have used a ripple or feather-and-fan edging.
This lady shows up in a collection of sontag photographs, but I don't think it really can be called that, as while it is clearly related, it doesn't wrap around the wearer, who has instead attached it at the neck, perhaps with a chain, and left the points to hang free like a short tippet.
I am not sure that this can really be called a sontag, either, as it doesn't wrap around in the same manner. This looks to me like she heard about a sontag and thought it was a good idea, but hadn't seen the illustration. (Or perhaps made it according to the pattern in the book and found out, like so many of us do, that it was too small, and just made do.) I do like the lacy border, though!
Oh, I wish this image was bigger! It looks very like the Godey's basketweave. The "wings" on this one are rather short, perhaps not even making it to the wearer's side -- which is just what the 1861 Godey's one does, where "the ends cross over the bosom".
In summary, the definition of a sontag or "bosom friend" seems to be a U- or V-shaped piece which lays over the wearer's shoulders, with the wings being long enough to either just meet at the waist (with straight ends) or, far more usually, to wrap around the waist, sometimes to the extent of meeting at the center back. Strings or cord of some sort are usually used to secure the wings, with those that are long enough being secured also with a button where the points meet at the back. There is always some sort of edging, often crocheted but sometimes knitted (perhaps also with a narrow crochet edging); the edging is usually in a contrasting color. The crucial element of a sontag, if you want to be a stickler (and don't we?!) seems to be its U- or V-shape, otherwise it is a variant of a hap or similar shawl (triangular or square folded cross-wise) that wraps around the waist and ties at the back.
(I doubt, by the way, that it was ever called a "bosom buddy", which I have seen lately. The word "buddy" first appears in print, according to Merriam-Webster, in 1850, just a little earlier than the sontag shows up, but I suspect that it would have been thought too slangy for ladylike use. The phrase "bosom buddy" first appears, according to Dictionary.com, in the 1920s, much too late for the sontag.)