The taper jig works well, but like anything requires a bit of getting to grips with.
My first big idea which was to attach the sandpaper with magnets works a treat. The strip is wrapped round the end of the jig and the magnet hold the end in place.
The modern magnets are ludicrously powerful and cheap too off E-bay (Got-Magnets UK, £4.50 for 5)
The clear polycarbonate (other transparent plastic materials are also available ;-) ) over the top also works well.
I used 80 grit paper which I buy from Toolstation on a roll, the clear plastic helps retain the paper too.
Clamping the jig down helps. As the arrow is moved back and forth and fed into the jig it can jam up, but that's the nature of pushing something into a taper.
It takes of material quite quickly, but 80 grit is about right, not too aggressive.
Doing the first end of the arrow as you can grip the other end which is still parallel in the electric drill chuck. You may notice I'm doing it with my little flight arrow head in place, trying to blend it in nicely, mind the steel point can jam.
Something I'm trying is putting a slip of card into the front end off the jig to cover the leading edge, which could cut rapidly into the shaft if you don't feed it in straight... (see pic), just done the other end of the shaft and the card slips work a treat.
To do the other end I gripped the shaft in my lathe chuck and had the arrow sticking out the back of the head stock. I rested the taper jig on the table of my pillar drill which was adjusted to the right height. For those without such exotic facilities a good wrap of masking tape and grip it in the electric drill would probably do.
If I'm honest I must confess that this is the second try with the jig. I'd got the first arrow made, but unfletched and thought I'd see how it flew,
It flew lovely and straight with no sideways flexing... Unfortunate, I'n nocked it too high an the string and it hit the target boss in a point down attitude and snapped. I had to split open the boss to retrieve the precious arrow head which I'd made at great pains.
A bit of an irritation but it teaches me a few things, the spine was fine, but the nocking point needs to be right for clean arrow flight for flight shooting. A flight arrow should really be landing from a nice stable flight of some distance, not a mere 10 yards.