Turns out that the explanation of this sinister observation is actually
rather benign: ABrowser preloads URL's that I visit regularly, and so my two
smaller domains dutifully record the accesses to Cpanel and several
associated .gif images, but my much larger third domain, hosted on a business
server, discards those extra access requests, which aren't even login
attempts.
On the other hand, my other browser, IceCat, doesn't preload any historically
visited pages, so the Recent Visitors logs in my two smaller domains don't
record any Cpanel vists when I haven't made any.
There have been no Cpanel visits from other than my own IP address; almost
all malevolent visits have been reflected in attempts to open nonexistent
WordPress files.