There is a debug option to print messages to stdout, it is a modparm to ruxc module, kamailio has to be started with logging to terminal, which is not the usual option for production, but can help troublesooting a bit. The plan is to add syslog support in libruxc, to be independent of Kamailio. However, this is better discussed in the ruxc project (https://github.com/miconda/ruxc), what the lib should offer for logging.
Not being related to kamailio code, I am closing this one here -- just open a new issue for the ruxc project if you want to discuss more, beyond syslog support.