Well, here's my 2-cents. Which just might turn out to be all my opinion in this case is worth. ;-)
Let's examine the item "logically."
The purpose of the hole(s) in the cylinder's sides is for a a locking-pin to hold the cylinder onto the end of a wooden shaft (or mounting-stub).
I agree with Charlene that the opening in the item's end appears to be too small for the usual size/thickness of wagon-horse reins. Those strips of leather need to be fairly substantial ...especially when they have to be long enough to go from the horse's front end, all along its back and rump, and then however much further from there to the wagon-driver's hands. If you've ever tried to turn a horse in a direction it didn't want to go, you know that a "heavy-gauge" leather strip is truly required (to match the strength in a horse's neck-muscles).
I've dug more than a few of another odd-looking brass relic, which I've been told does what some people here are saying a whiffletree does. The item is an (approximately) 5/16-inch-thick brass ring about the diameter of a half-dollar, which has a 1&3/4-inch-long 5/16-inch-diameter "stem" that has a small circular "collar" and a threaded tip. Supposedly, it was mounted on the upper part of a wagon-horse (or mule's) body-harness, to keep the reins from dropping down, while also keeping them "free-moving." (I wish I had a picture, but I don't, so I'm trying to point you a picture with words.)
Envision this: When you rig your horse(s) to the wagon, you put the reins from the horse's head through the ring-thing mounted on the horse's harness-gear and then pull them (the reins) back to the wagon-seat.
Note: some of today's lawnmowers have a similar ring-thing mounted on the mower's long handle-frame, to keep the starter-cord up on its path from the engine to near the the "handlebar."
Now, if Charlene's brass relic is indeed a flagpole-tip/guidon-tip, the hole at its end could be for attaching "honors" (ribbons). The hole is about the right size for those.
I'll "stay tuned" here, to find out which theory about the relic turns out to be the correct one. : )
Regards,
TheCannonballGuy
Regards,
TheCannonballGuy