Would definitely like to know.
OK, to begin, we should take another look at the picture above of the original bayonet scabbard. Notice the two indented areas at the top of the brass tip with what looks like the heads of two brass nails sticking up?
Those aren't two nail heads, but the ends of a brass round/wire that was bent formed into a "U" shape. The base of the "U" is below the surface of the leather side the brass tip and the ends of the "U" go up through the leather and through two holes in the top of the brass tip. Then the ends of the "U" were then peened over to attach the brass tip. It was a rather simple solution to attach the brass tip, though it is a bit of a PITA to do it at home and for only one scabbard at a time.
I must say I have never found original instructions on how to attach the brass tips, but have seen a LOT of original brass scabbard tips broken off with the leather and "U" shaped wire inside. From examining those original broken off tips, I figured out a way to do it for repro scabbards - though my way may not have been the exact way they did it.
First you have to get a piece of brass wire. I found some welder's brass brazing rod from our shop that was almost the exact size from measuring originals. It's been so long I'm not sure if the diameter was 1/16" or 3/32" and one rod will make many of the "U" shaped wires. (I think I used the 1/16" size rod for bayonet scabbard tips and the 3/32" for sword tips.) If you don't know a welder who will sell or give you a single rod, here is where you can find some rather inexpensive brass rod to use, which some hardware stores or hobby shops carry.
1/16"
https://ksmetals.com/products/brr-1-16
or
3/32"
https://ksmetals.com/products/brr-3-32
OK, then you need a wire size drill bit that is slightly larger in diameter of the brass rod to drill the two holes in the top of the new replacement brass tip. I can't remember exactly how far apart I've drilled the two holes and don't have an example at home to check, but I think the distance was about 3/16" between holes. If you have access to an original or repro attached scabbard tip, I suggest you double check the measurement.
Now this is important: I strongly recommend you whittle or cut a piece of wood so one end goes pretty far into the brass tip and fits a bit loose inside. The other end should be about three or more inches beyond the tip. Do this before you drill the two holes in the brass tip. Make sure this wood is inside the brass tip before you drill it. This will help you make clean holes in the brass tip and hopefully stopping before you drill into the opposite side of the brass tip. Save this piece of wood as you will need it later.
I hand bent the wire into the "U" shape COLD (don't heat brass rod to bend or form it) around a 3/32" pin punch with my bare hands and that's easy to do. (I've seen originals that were either rounded or flat on the bottom of the "U" shape.) As I remember, the "U" shaped wire was about an inch long before bending, so there was enough room for both ends to go through the leather and tip and stick above the tip on both sides.
Before you try to peen down the ends of the "U" shape rod/wire, you have to have something to act as a mandrel inside the scabbard and tip, to have something solid to peen the ends of the "U" shape rod/wire against. I don't remember if I used a good sized pin punch or large screwdriver to act as the mandrel and you should lock the end of whichever you use into a vise to hold it when peening. Or you can use the bayonet blade as a mandrel, but I don't recommend that.
OK, so start stitching at the small end of the leather you are going to make into the body of the scabbard. You put about 3/4" of the small end of the scabbard inside the brass tip and if you need to, shave some leather off the outside to get it to fit in that far. Then stitch along three or four stitches beyond where the leather sticks out from the top of the brass tip.
Now put that piece of piece of wood inside the leather and brass tip and drill through the two holes you previously drilled in the brass tip and into the leather inside. You need to drill into the wood a bit to ensure you have clean holes in the leather. Then take the wood out and find what you have to use as a mandrel.
Now put the now drilled through leather back into the brass tip and try your best to align the holes up. You have to get both ends of the "U" shape rod/wire through the inside of the leather and up through the leather and brass tip. I bend the "U" shape rod/wire sideways into a slightly bowed shape to do this, though they might have cut the ends off and used a long pair of pliers to get both ends up and through the leather and tip. (Expect to do a little cussing the first couple of times you do this! LOL) Once you have the ends up and outside the tip, get whatever you are going to use as a mandrel inside the leather and brass tip. Cut the ends off a bit above the outside of the brass tip and bend or hammer them a bit towards the front or back to hold them and then peen the ends into little heads. BTW, you may and probably will need to re-wet the leather at least once while you do this and finish sewing the body all the way to the top.
OK, need to give my arthritic hands/fingers a break, but will come back later to explain the modern way to affix the brass tip.
Gus