in this case make sure to enable DEBUG for the binding
https://docs.openhab.org/administration/logging.html
This should work (creating rachio.log with DEBUG info):
# rachio logger
log4j.logger.org.openhab.binding.rachio = DEBUG, rachio, osgi:*
log4j.additivity.org.openhab.binding.rachio = false
# File appender - rachio.log
log4j.appender.rachio=org.apache.log4j.RollingFileAppender
log4j.appender.rachio.layout=org.apache.log4j.PatternLayout
log4j.appender.rachio.layout.ConversionPattern=%d{yyyy-MM-dd HH:mm:ss.SSS} [%-26.26c{1}] - %m%n
log4j.appender.rachio.file=${openhab.logdir}/rachio.log
log4j.appender.rachio.append=true
log4j.appender.rachio.maxFileSize=10MB
log4j.appender.rachio.maxBackupIndex=10
The config file for logging is org.ops4j.pax.logging.cfg located in the userdata/etc folder (manual setup) or in /var/lib/openhab2/etc (apt/deb-based setup).