Good afternoon,
As a general rule plumes are longer and straighter than hackles.
Hackles are usually made from chicken feathers but can be horsehair, particularly the guards regts. They are worn mostly by infantry regts and have a wire loop at the bottom to fit on the beret behind the cap badge.
Plumes are usually made from horsehair but can be feather. Some are extremely long, household cavalry and dragoons, and flow downwards from the helmet. The bottom has the peg type bottom end like yours, this fits into a socket built into the busby. Hussars, RHA, RAF band etc.
I can find no reference to a red over black one for the british army but have not yet found anything on yeomanry. The only one that colour I have found is in the Pakistani army. It is possible that someone in your family served with them, officer or warrant officer rank and maybe senior NCO.
So I would say yours is a plume made of feathers. Scots regts who wear a hackle usually have them made from blackcock tail feathers hence the distinctive curves turning outwards.
Hope this helps you, John915
