I am not exactly sure how to wire it, but the "mysterious black box" is the float switch, which actually turns the bilge pump on. The power for the pump should run through the float switch, not straight to the pump, that way if there is no water in the bilge, the pump won't come on. It sounds like your pump is direct wired to the power, thus it runs all the time.

It sounds like from your description that the brown wire going to the pump should be removed and attached to one of the brown leads on the float switch. Then attach the other brown wire from the float switch back to the pump where the other wire was removed. Make sense?

Just make sure the float switch still works properly too. If you have it on the trailer, put the plug in and then run a garden hose into the bilge to test. It will take more water than you think to trip the float switch though, like 2" of water, so it will take probably 10 gallons of water or more.

Good luck.