Have you tried to set the Zammad log do debug?
vi /opt/zammad/config/environments/production.rb
Change config.log_level = :info
to config.log_level = :debug
restart zammad and see if there is more information in the log file
Once done, turn it back to :info
And another thing, install and set up logrotate
since the log does not automatically rotate or compress, here is the task for ansible