Rsyslog outputting to custom log file

Well I finally figured it out. I wish someone had answered this for me. Took several days to figure out what was wrong, but I guess there just aren't very many people on superuser.

The issue was with the file permissions of the custom log file as I originally theorized. I thought I had the permissions correct, but it turns out the owner needs to be "syslog" and the group "adm". I determined this by comparing to the user.log file. Once permissions were modified and tested again, all works perfectly! I hope this helps someone else out there quicker than I was able to find answer.

Here are the final permissions

-rw-r--r-- 1 syslog adm 0 Aug  3 05:09 anm.log