Hi, Ricky,
A practical way to make up a replacement taper pin for a swivel jaw vise would be to cut/file that taper in a scrap of sheet metal, filing til the part will fit the taper with no 'rock'.
This, read with a protractor, gives you the angle from centre-line. Use this number to set your lathe compound, and turn that taper on a scrap of steel round stock, (common mild steel is perfectly adequate for this part) taking care to have a good smooth finish.
Try the turned taper in the vise jaw. If it doesn't 'rock' and marks full length, the taper is correct. If not, adjust your compound, and try again.....a small fraction of a degree will make quite a bit of difference in the taper fit.
Correct the angle as necessary, for an optimal fit in the taper bore, by polishing with 320, then 400, then 600 emery. 600 will bring up an adequately good finish.
Personally, I prefer to drill/tap the taper pin, once done, and fit a small forged eye-bolt, then do a light weld or braze to retain the eye, and blend for appearance. This forms a little ring at the top of the taper-pin, which allows the use of any drift or round stock to loosen the taper pin when needed.
cheers
Carla