Credentials: I'm a decent hobby cuemaker, & professional woodworker & machinist. IOW, won't pretend to tell you what sizes, etc or anything else is "better" for cues, but can suggest what's available. See my previous, post: ideally threading would be done on an engine lathe or other leadscrew threading equipped machine. You will end up spending a lot on high end products (taps, dies) that are difficult to attain tolerances needed for cue making, though the tools can be contrived to work, more or less, if used appropriately in a lathe.
Caveat out of the way:
Here's a page of split dies. They can be set open (or broken

) with the adjuster screw. Then incrementally decrease the spread until the sample/test parts fit snugly. There may be cheaper sources on Amazon. McMaster-Carr is another source.
Round Adjustable Dies
www.kbctools.ca
Looking for taps? KBC Tools & Machinery has a comprehensive selection, including spiral pointed taps, STI taps, and tap and die sets. Shop our range of taps now!
www.kbctools.ca
McMaster-Carr is the complete source for your plant with over 595,000 products. 98% of products ordered ship from stock and deliver same or next day.
www.mcmaster.com
Obviously, search the pages for other sizes.
Something like this should be shop made to fit the taper in your tailstock. It needs to be dead concentric with the die mounted.
This one won't work, unless it can be modified in a cylindrical or Tool & Cutter grinder to make it a taper shank that fits the lathe TS. There's too much overhang to use in a chuck in the TS, though with flats on the shank and loose jaws in the chuck, it could be made to function as a floating die holder. Even at that, note that the provided shank is 3/4" dia, so metal machining facility is needed to adapt it. But you might be able to come up with something similar made in your own shop..
KBC,1.1/2 IN.ODX3/4 IN. SHANK DIE HOLDER,1-528-005,KBC Tools & Machinery
www.kbctools.ca
If a non-floating holder like above is used, the TS has to be loose on the ways. You turn the headstock of the lathe by hand, and with the other hand, control the TS from twisting but help it slide along. A floating die holder is better, if you can make one - the sliding is incorporated into a 2-part keyed shank.
Note that with this style die holder, the depth that can be attained on the part is limited by the depth of the die in the holder, and any extra depth or back relief provided in the holder.
Here's taps. I believe spiral flute works better in wood (or steel).
In steel, they pull the chip out, as for threading blind holes.
Spiral Flute Taps
www.kbctools.ca
However, if you have a way to drive them under power, gun taps have advantages in metal and are cheaper in through holes.
https://www.kbctools.ca/CatSearch/95/spiral-pointed-taps/1?v=j&facet=[["Fractional Size","Fractional Size","5/8\"-11"]]
Most cue joint thread taps are not common machine tap style or sizes and need to be bought from cuemaker/billiard supply houses such as Atlas.
Keep in mind that if the cue you are working on was made by someone with an engine lathe, the taps & dies you buy to match might or might not provide exactly the same thread. With an engine lathe any thread pitch can be applied to any diameter. If a guy wanted. for what ever reason including his own perception of "hit" and/or say, balance, (thinner steel wall) the joint ferule could be made .657-10 if he preferred and was making both parts.
Also, above listings are just examples. If you find them cheaper on Amazon, it will probably be OK for wood cutting. The higher cost tools are for people running production lots in difficult materials all day long & have material specs and surface treatments that are irrelevant to wood, or to cutting a few pieces of steel.
smt