So, basically you do not have a float switch that activates the bilge pump and the only way to evacuate water is manually, via an on/off switch.
If the pump works and when testing, water is seen being ejected from the through hull, then there is no need to replace the pump. Take a trip to your favorite marine supply store and pick up a coil of marine grade wire - which should be stranded copper - tinned throughout, not just at the ends.
Also pick up a Rule float switch, either with Mercury or the newer mechanical type, along with a three-position switch. There is a wiring schematic provided with the Rule switch, which shows several ways of wiring the switches.
It's a very easy and quick project to do, if you have all the materials collected before doing the job. Make sure you use marine grade wire connectors and shrink-tubing.
True Blue . . .
sold the Nauticat