At last I have something to contribute.
I made a drill chuck arbour for a Super Adept and also a live centre for the same.
From memory the taper is the small end of a "0" morse. The only practical way to do the taper is by trial and error. Start with the top slide at 1 1/2 degrees and keep trying in the TS quill.till you get the right taper. Permanent markers like Sharpies are excellent for testing tapers. Once you get it right, do make a few spares!
I would not suggest using the ball method for checking this particular taper, there is too much of a chance to get them stuck in the hole, besides if you don't have a taper turning attachment there is little point.
I would put up some pictures of the live centre but the wretched thing was so small that it slipped out of my pocket and got lost, the only proof now of its existence is a picture in the SMEE journal and i can't find that issue either. Shame it got lost, it really was a sweet little thing all in stainless (except needle and thrust bearings), much too small to allowed out by itself, but such is life.
Ned Ludd