On my boat, and many others, the bilge pump circuit has a small LED light that is on when ever the circuit is on. The pump will still not turn on until there is enough water in the bilge to lift the float, or in some cases the pump will cycle on every few minutes.
Here, do this. Take garden hose, fill the bottom of the boat with enough water to cover the bilge pump. Turn the switch on. If the pump removes 90% of the water then everything is great. If it doesn't, fix it.
Kill two birds with one stone. Throw some soap in and wash the bilge while you are at it.