Well, we now know that this mystery-relic comes in at least two significantly-different sizes.
I think that fact is important when we try to figure out what it actually is.
I noticed that the reported size of Charlene's (at 4" long, 1-&-1/2" wide) is much larger than the one in Rasrandy's photo, which is only as wide as his thumb. So I measured one I have, and it is (precisely) 3-&-7/8" long, 7/8" wide. It fits exactly on a 3/4"-diameter wooden pole. That means the smaller version of the relic is very unlikely to be for a military flagpole - even a cavalry guidon - because a 3/4" round wood shaft is very easily broken. Heck, even a typical modern household wooden broomhandle is 1" to 1-&-1/8" in diameter. So I have serious doubt about this relic being from a MILITARY-USAGE flagpole. (Combat-conditions are rough on equipment, y'know.)
Charlene, what is the diameter of the hole (that a shaft would fit into) on your relic?
But we do know for certain that whatever the relic might be, it DOES go onto a round wooden shaft of some sort. Besides them all having a small hole (near the open end) for a mounting-screw or nail, Rasrandy's still has some wood inside it.
I think one other key ID-clue would be the "arched slot" on the end of the relic. I'm describing it as a slot because it's narrow in comparison to its length. On my relic that slot is only 3/8" long - and a bit less than 1/8" wide. So it seems to me that the slot is for a thin strap (or cord) - to hang the item from a hook or nail on a wall.
I happened to notice that my wife's umbrella has a similar thing on the end of its shaft - with a thin strap going through it. for easy carrying - or hanging.
Or the relic might be from broom-handles (of various sizes) - or some similar wooden-shaft household tool that you might want to hang from a wall. (A broom is best stored with its bristles off the floor, lest its own weight cause the bristles to mushroom outward.)
I think another relevant ID-clue (for deducing the relic's time-period) is the fact that it is a "one-piece" item made from solid-cast brass ...rather than being fabricated from sheet-brass (like, say, a bayonet scabbard-tip is). This makes me think the relic is more likely to have been made during the Colonial-to-early-1800s era, instead of the 1850s-1860s.
I hope one or two of my "logical deductions" about the relic will be helpful as we What_Is_It Forum denizens try to figure out what it is. ;-)
Regards,
TheCannonballGuy