Think in terms of a machinist in the 18th century and how they cut threads. Screw cutting lathes were either non-existant, or very rare (depending on time period). A machinist would have cut the threads in a very simple lathe without benefit of lead screw, change gears, or even a slide tool rest. They may have roughed the thread out using a single point tool and establishing the pitch of the thread by eye/experience and maybe some chalked lines on the work to set off the pitch of the thread. They may also have had a multiple-point cutting tool which was filed out of flat tool steel and had more precise pitch and form. Either tool was used on a tee rest.
Internal threads were cut in much the same manner, with a single point tool having a 90 degree bend between the shank of the tool and the actual cutting section, and the same sort of multiple-point tools adapted for internal threads were used.
Taps and dies were often made by individual machinists using these same methods for cutting the threads on them. The result is the pitch of a thread cut by these methods may approximate a 'regular pitch' such as a lathe or tap or die would cut. Thread form was also a non-standardized thing in those times, maybe a larger shop might have set their own standards for form and pitch, but there was no across-the-board standardization.
My thinking would be to grind a form tool- my own preference is to use high speed steel- and try to match the thread form on the bolt. Not everyone has access to optical comparators. Thinking like a machinist of olden times, I'd likely get a piece of thin steel and file a thread template gauge, using the threads on the bolt as the 'master'. With a magnifying glass and some careful filing, a template gauge could be filed out. The tool bit for cutting the threads is then ground and stoned to match this template gauge.
I'd grind two tool bits- one for cutting male threads, and a small boring bar for cutting the internal threads. The external threading tool is mainly to check your work. I'd cut a sample external thread and try it against the original bolt as a kind of 'thread profile gauge'. This will tell the tale as to whether the lathe is cutting a pitch that matches, or very nearly so, the original bolt.
Chasing a thread using a graver or multi-point tool is something I've only read about. Never seen it done, let alone have I done it myself. Back in the day, this was a skill many machinists developed. I wonder if anyone is still amongst the living who can cut accurate screw threads by these old hand methods. As for the class of fit of mating threads cut by these methods, it was probably all over the board and varied with the skill of the machinists. Taps and dies made by these methods might actually have had a better chance of getting a closer fit if the tap was used to cut the internal threads in the die when it was being made.
We take so much for granted at every level of our lives. Lathes with quick change gear boxes for threading and feeds are almost universal, while the 'loose change gear' lathes are mostly antiques or relegated to home shops. Most people who operate lathes have likely never had to make up change gears to cut a particular thread.
Every so often in my engineering practice, a job will come along to do some design work for either the repair or re-creation of some historic old mill or machinery. I get told: "Think like 1840 (or 1890)" or whatever era the original mill or machinery was from. It's an interesting exercise to write off using welded fabrication (or at least none that is visible), designing cast parts, and avoiding the use of vertical milling machines. The job Rivett608 has posted about is one of those jobs that put me in that 'think like the 18th century' mode. I am lucky: the historic engineering work I get into is usually from the late 1800's, and is big enough and 'loose enough' that methods such as blacksmiths and millwrights used are close enough. Matching a smaller screw thread, let alone a female thread, is a good deal tougher than anything I've tangled with.
Hopefully, a standard pitch of thread that a lathe can cut will match up close enough.