Thanks for your enquiry,
If the lithium auxiliary battery is fully charged the BCDC will be outputting very little current meaning that very little charge is being taken from the start battery. This then means the start battery will hold its voltage for a longer period of time. It may take up to a couple of hours before the voltage drops to 12.7v where the BCDC will switch off. Keep in mind that the BCDC will check the start battery's voltage every 100 seconds.
If you are running a lithium start battery the voltage may not drop below 12.7v keeping the BCDC on at all times. In this case it is required to fit a solenoid or high current relay.
For any further questions, your more than welcome to respond to this email or contact our technical support line on 1300 REDARC (1300 733 272)