A rein-guide is mounted on a draw-horse's main harness, so rein-guides always have a stud-shaped projection. Therefore, your find is not a rein guide. It is one of several varieties of gag swivel from a horse's bridle-&-bit harness. See the scan (below) of a page from the 1909 Pittsburg Harness Supply catalog, which shows a slightly different variety of gag swivel. (That scan was originall posted here at T-Net by BigCypressHunter.)
The other photos show a rein-guide, and how it is mounted on a draw-horse's main harness.