You are probably saving a little money, but I hazard that it isn't much unless you are in a very cold environment. We leave ours on when we are boondocking because we don't want to wait for hot water in the morning for our ablusions.
To see if your water heater is kicking in at night, turn off both propane tanks. When the HW tries to light and fails because of no flow, the red light on the panel will illuminate indicating a fault.
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