The hour meter should be running whenever the key is on. I believe most hour meters are powered by the ignition coil power feed which should only be on if the engine is running OR the key is turned to the run position.
Not so with the OEM Rinker gauges. The Hour meter on the gauge only is triggered when any sign of RPM is registered. If the engine distributer does not send a signal, no hours. Simple as that. You can also double check your hrs by checking the ECM. Al