Here's another way to make small balls from brass.
This ball is 7/16 inch diameter.
Grind the teeth off an old file keeping the file flat and cool.
Drill through the file with a carbide drill, or end mill to the finished ball size. Keep the file cool.
Slot for the shank with a cutoff wheel, or carbide mill.
Grind the cutting face maintaining flatness to touch up the edges.
This tool can also be made from tool steel in the soft, then hardened and tempered in the cutting area.
If done in the soft, one of those hand taper reamers will give you a bit of clearance under the cutting edge.
A Dramel tool can also be used to make a little clearance under the edge of a file.
Now, place a rest as shown in the lathe tool post, or like a wood lathe rest, for the file.
A drill press may also work?
It's easiest to do if you rough out the shank area with a parting tool, and cut the od close to size.
Gently, with the lathe turning slowly, feed the file over your blank.
The sharp corners of the file will shave the blank down to a sphere.
The file will drop over the ball and hang there.
Remember files are brittle, and will shatter if forced.
Use eye protection, preferably a face shield to cover the neck area too.
Use a bit of cutting oil to cool things off.
Now, saw the ball off and dress the stem to blend with the od.
I do not recommend this procedure, but post it is an old time way of doing things.
Safety wise, it would be a good idea to draw (temper) the unused area of the
file to a straw color making it more flexable.
Kap