Horse Tack: Cast Iron Fitting, Much Wear; Whatsit Called?

The part that goes over the end of a wooden shaft is about 1 1/4 inches inside diameter, an' about the same depth. The amount of wear seems to indicate long, regular use. The hook has a tee at its tip, perhaps to prevent uncoupling under slack load.
Somewhere on a working horse's rigging, an' almost certainly matched by another identical on the other side of the tack, this had a specific purpose...an' was known by a name. It may have been part of a buggy or cart, rather than of the harness on the horse (or mule).
I'll be grateful to hear what y'all think of it, an' Thanks for lookin'!

 

Might be a singletree/single tree yoke end cap.

"A single tree goes behind a single horse and hooks to the harness and then to the load. It often has a hook on each end to fasten to the trace chains and in the center of the single tree there is often a small ring for fastening a clevis or chain, etc."
https://museumoflocalhistory.org/ex...ingle tree goes behind,a clevis or chain, etc.


https://www.etsy.com/listing/1313918266/vintage-single-tree-yoke-endcaps