On ubuntu, I had to also comment out the drop privileges lines in order to get the rsyslog to actually read the log file outside of /var/logs.
#/etc/rsyslog.conf$ModLoad imfile$InputFileName /data/mysql/error.log$InputFileTag mysql-error$InputFileStateFile stat-mysql-error$InputFileSeverity error$InputFileFacility local3$InputRunFileMonitorlocal3.* @@hostname:<portnumber># Set the default permissions for all log files.##$FileOwner syslog#$FileGroup adm#$FileCreateMode 0640#$DirCreateMode 0755#$Umask 0022#$PrivDropToUser syslog#$PrivDropToGroup syslog