Would "something" fit, for instance, a process [ Console2 ] which started our Perl process, and then delivered a Windows Message to this process, and Perl, not knowing what to do with this message, invokes the signal handler established for SIGHUP?
No. I downloaded the source for console2 and the string "SIGHUP" does not appear anywhere in it, so your log message does not come from that.
As I said, I don't believe there is any way for a perl process to ever invoke a SIGHUP handler. Which only leaves your perl script to be the source of that log message in response to some stimulus other than a sighup. (ie. user error)