OH good, thank you David. That saves digging, dismantling, and measuring. I'm pretty sure the threads are the same across the different versions of the mount. Determining the right original configuration for a given version might be more difficult than the thread pitch.
Most of these are two piece. The standard DSC on grey GEM pier is two piece. I have not seen a one piece rod on a grey GEM version yet. Some early Edmund 1" shaft GEM mounts (same series as the 5/8" shaft) had a screw in reduction to 5/8". That 5/8" reduction part was very long. The picture in entry #6 looks like a combination of both type mounts, and the picture looks like an original Edmund printing.
What the OP shows in the opening entry is a standard later version DSC grey GEM but on a tripod instead of pier. The earlier versions had different setting circles. There were a lot of versions. I have all these and will take pictures tomorrow, Sat. Too late now. I'll also measure the length of the smooth part of the extension.
Use a little caution. The idea of extending a 5/8" rod with a 3/8" thread, and hanging a counterweight on it, wasn't exactly a top notch idea. For the most part by far - it works well. I haven't had any issues. However, I have seen some that were bent or destroyed at the threaded junction.