Turns out the charger and the fence are working fine. No, I didn’t grab on to the terminals with each hand to find out, but was about ready to.
Brought the charger into the house and took off the cover that houses the battery. Checked the voltage of the battery. Rated for 6 V but emitting 7 V. Good. No serviceable parts inside. Put the battery back in and closed it up. Used the tester with the charger on the table and: light dawns! That clicking the charger makes isn’t just an audible clue that it's working, it’s also timed that each click means that a 10,000 V (or whatever) pulse is being sent out the + terminal. In the comfort of the kitchen and without full sunlight in the way, I can see the little tiny lights on the tester light up with each click.
Put the charger back on the fence and at this time of day one part of the fence is in the shade. I can just barely see the lights come on when testing that part of the fence. Will have to try other parts of the fence this evening when it gets darker. I didn’t realize (1) the charger sent pulses and (2) the friggin’ lights on the tester were so dim.
So I guess the bit about digging a trench for the ground rod works OK. I hived two packages inside the fence on Sunday and since the fence has indeed been working it’s probably why the bears haven’t gotten them. I was afraid the sugar water would attract them. Or I was just lucky, since the fence has not been baited. The bear(s) took apart my hive from last year, and it was sitting only 20' or so from where the fenced area now is. It’s two 10-frame deeps and he ate what was left of brood comb and some honey. Amazingly, only 3 of the frames were damaged, the rest of the hive is just fine. A couple years ago we had one bear, and later a bear with a cub, that would head north through our front yard every morning and then back south in the evening, apparently commuting to work. Try my hives now, Pooh!
On to the next problem...