Put a caliper or a micrometer on it. 14mm is more like 9/16" than 5/8". I should think it would be an imperial thread but if it does turn out to be metric then it will more likely be trapezoidal than acme.
You can't tell by looking at it. There's only 1 degree included that's only half a degree per side difference. Put a mic on the OD or a ruler across ten pitches.
Incidentally, this is my list of vice restorations.
Found a little billet of bronze (I suspect!) to make up a new nut.
Bought an inch of meehanite/cast iron to make up a retaining ring for the Swindens.
The little "Nippy" (it isn't actually the Nippy brand) vice, fresh from the dip just needs some light fettling.
And that hewge bar of found copper <proud> is going to get chopped up to make soft/welding jaws fro the Swindens. Just as soon as I get bored polishing it
Unless you can measure the thread angle accurately it'll be a guess. The thread standard for 5/8 ACME is 8 tpi. For 16 mm it is 4 mm pitch. Assuming a standard thread it sounds like ACME. Re the tap, I've had no experience of using one, but there are various threads I've seen in the past that suggest it's an almost impossible job to get a single tap through. However, Tracy tools sell them. The thread you have is right hand BTW. - http://www.tracytools.com/5-8-x-8-acme-taps