The shape of the body suggests it was made for use on a particular lathe, and the lack of a name bears out Keith's suggestion, so this specimen could well have been made by an individual turner or apprentice. Or indeed by a fellow model-engineer long gone before!
Another common design for these, strips the needle mounting back to a circular gimbal.
Both forms are in L.H. Sparey's The Amateur's Lathe, p.70, ("The Centre-Finder"
with a photograph of the type Norfolk Boy shows, and a drawing of a much simpler, nay minimalist, version of the ring-gimbal.
In one respect it is more versatile than a DTI. Its purpose is in centring by a centre-pop, so the outside of the work-piece can be any shape, such as a plate, irregular casting or rough cylinder. A DTI can only work as a centring tool on a cylinder with a good-quality surface.