Years ago I owned a couple of Parker Hale cleaning rods and also some jags and brushes that fit them.
I do remember that they used a different thread to other rods.
I would have thought they "could" be BSF, or B.A. which were sometimes/often used by the Poms way back when.
As you say, the combination of .198" and 27-28 tpi is a strange one.
Nearest BSF thread would be 7/32" X 28 tpi, but this has a major dia of 0.219" or thereabouts.
Could the major dia of your thread be worn or undersize by that much.

No 1 B.A. thread is 28.2 tpi and .2087" major dia.

No 12 UNF is 28 tpi and .216" major dia.

Here is a link to a heap of thread types, maybe it might help.

http://www.watchman.dsl.pipex.com/thread.html