Ah, yes. That's better :-)
(In the real project, I'm going to pull the guts out of "b.cgi" into a new "c.pm", and have both a.pl and b.cgi use c.pm to do the heavy lifting, without needing to mess about with having a.pl capturing output from b.cgi)
Thanks for the tip on CGI.pm, too. $DEBUG was actually set to 1 (meaning that this *should* have worked...) I still don't know why it didn't work, but I learned something new today, and that's always a win.