I agree on that test but also try the manual oil fill override switch on the motor. If the primary oil tank ( on the motor) is low, try holding down the manual switch. Ignition must be on but engine not running. You should be able to hear the oil pump in the secondary tank (in the bilge) and the tank on the engine should fill up. If it does, you have a sender issue on the main tank, a bad connection or a bad controller.
If you hear the pump working but the tank doesn't fill up, you probably have a clogged line or pump. The screen(filter) is the more likely cause.
If you don't hear the pump, you have a wiring problem or a bad pump.
Since it seems that you get oil when you rev up, the only thing that changes is the voltage out of the alternator. That could make the pump run harder which might also indicate a clog. Note that if you get the alarm while trolling, shut the motor and remove the cowling to see if the tank is empty ( well almost empty) If not and you have the alarm, it could be a bad sensor or wiring.
