Correction and followup...
I am actually configured to do extended logs, not 
debug logs.

Below is a clip after I canceled.  The interesting 
part is the 'from'...it appears a GIF file is calling 
an HTML file...huh?...normally HTML calls GIF not vice 
versa.  It seems the webserver is responding to all 
requests, regardless of what they are, without error 
messages.

Is this confusing HTTrack?  That doesn't appear to 
answer why the 'near' option is still letting HTTrack 
go yet further than the bad link.  (I see 'near' as 
being a way to get all non-HTML files from external 
sites one-level deep).  Is 'near' the 'leak' to the 
2nd domain?
06:12:54 Warning:  File not added due to mirror 
cancel: www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/resources/default.htm06:12:54 Error:  "mirror 
stopped by user" (-1) at link www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/resources/default.htm (from www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/tiem_watermark.gif)
06:12:54 Warning:  File not added due to mirror 
cancel: www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/Best_of_1999.htm06:12:54 Error:  "mirror stopped 
by user" (-1) at link www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/Best_of_1999.htm (from www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/tiem_watermark.gif)
06:12:54 Warning:  File not added due to mirror 
cancel: www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/sections/feedback.htm06:12:54 Error:  "mirror 
stopped by user" (-1) at link www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/sections/feedback.htm (from www.the-internet-
eye.com/downloads/HOWTO/_themes/internet-
eye/tiem_watermark.gif)