So you are saying if the ski is on the trailer for a week, the pump will still search for water and wear down the battery.
Many pumps are designed to by cycling pumps. So are wired to operate ONLY when the motor is running and other run 100% of the time. Thus, the direct wired will cycle at whatever rate they are programed to cycle. So yes, they will kill the battery over time.
Conflicting concerns. If you wire it to have power when the motor is running, the it is not safe at the dock while not running... The other option, come back to a dead battery.
I would suggest wiring them to a float switch. This way they will not operate if there is no water. Therefore not kill the battery. If there is water, the pump will cycle...