1. Installed BNC connector on VOR/LOC antenna.
2. Once I had it done, I checked it with a continuity tester, as I always do. I was dismayed to find that there was a short somewhere between the back seat and the VOR cat's-whisker antenna at the top of the vertical stabilizer. I traced the defect to a segment that runs up the between the VS, so I cut out the bad segment and managed to fish through another section of RG-400 coax. I will crimp some new BNC connectors and hope for the best.
[Postscript: As it turned out, I didn't need to replace the coax. Doing a continuity check only works if the coax is not connected to the antenna base. But at least I upgraded the old RG-58 in the tail to RG-400. So not all was in vain.]