To keep the chassis battery charged I would recommend the
BIRD a Bi-Directional Isolator Relay Delay
It charges both batteries when either one is
being charged. When the coach is being driven,both
batteries will be charged from the engine's
alternator. When the coach is plugged into shore
power,both batteries will be charged from the
converter. If neither battery is being charged, the
batteries are fully isolated. The controller also
senses heavy loads on either battery to prevent
the wrong battery from being inadvertently
discharged.
While sitting even while plugged in, if some type of charger is not hooked up to the Chassis battery it will go dead from the parasitic loads.
I keep mine plugged in all the time at home and with the BIRD both Chassis and House batteries stay charged.