I just had a look on my Wheezy laptop (where I have it installed and working) and I can't see any specific log files for tklbam-squid (or anything tklbam much). TBH I can't find much about it at all... :(

But looking over your stacktrace again I just tried to launch squid-cache to get a feel for what might be going wrong.

$ /usr/lib/tklbam/deps/usr/sbin/tklbam-squid
error: incorrect number of arguments
Syntax: /usr/lib/tklbam/deps/usr/sbin/tklbam-squid  
Runs a squid instance to cache TKLBAM's duplicity archives
Arguments:

             [hostname:]port (e.g., 3128, 127.0.0.1:33128)
             Size of squid cache (can be absolute or relative size)
        
                        1000MB - 1000 MBs
                        2GB - 2000 MBs

                        50%                                                  of free space in spool location

Environment variables:

    TKLBAM_SQUID_CACHE_DIR      location of cache dir (default: /var/spool/tklbam-squid)
    TKLBAM_SQUID_USER           user under which we execute squid (default: proxy)
    TKLBAM_SQUID_BIN            path to tklbam squid binary (default: /usr/lib/tklbam/deps/usr/sbin/squid)

Do you have plenty of free space? I wonder if that might be the issue? Although I'm only guessing really...

Regardless I'll email Alon & Liraz. TKLBAM is actually Liraz's baby so I'm not sure if Alon will know. Liraz will but he is in "dev mode" and is notoriously hard to get hold of... I'll let you know...