I finally solved the problem with the cable I was trying to make to interface my VX-8GR with the computer, as described in my last post. As I had begun to suspect, the trouble was caused by the 2.5mm jack plug not fitting properly in the VX-8GR data port socket.
As suggested by one of my readers, I tried the cable in the COM port of the TH-D72. Although I couldn't figure out how to make data appear on this port, I did see some output when turning the TNC on and off which suggested my cable did work.
I then tried it back on the VX-8GR and used my oscilloscope to look for anything digital. I didn't see anything. I then tried another 2.5mm jack with the sleeve off so I could get the 'scope probe on the solder tags and with a firm press it went in with a click. I now saw -5.6 V on the TX pin - clearly an RS-232 signal level.
The jack I originally used had a plastic sleeve or cover and the diameter of the base was just a bit too much to allow it to go all the way in. One with a metal sleeve had a slightly smaller diameter base. The metal sleeve itself interfered with inserting the jack, but I could put the plastic sleeve on that jack and it would still go in. So that, finally, is what I did, and I now have a VX-8GR PC cable that works. It also works with the COM port of the TH-D72 should I find a use for that.
As a ham and electronics enthusiast I don't believe in buying things I can make myself, but sometimes making it yourself can turn out to be more trouble than it is worth!