Float switch sensors on waste tank

Hi, I have a 2013 Swift Autocruise Alto fitted with a Sargent EC400 control unit. The waste tank has two float switches in it, one for half full, one for completely full. There are two corresponding leds on the control panel. The half full indicator works occasionally, the full indicator does not work at all.

I have removed both float switches and tested them. They both work perfectly.

So I am left with a wiring problem, or a problem inside the Sargent unit.

So I am looking to replace the cable between the Sargent unit and the sensors as a cheaper option in the first place.

At the sensor end, one of the connections is common between the sensors. When I meter the common cable going back to the Sargent unit it does not appear to be connected to ground, or to +12V, which suggest the problem is in that cable. The signal cables to the sensors are obvious at the Sargent end, however the common cable is not. I think that must be (or should be) connected to ground or +12V at some point I cannot see.

So, my question is, does anyone know whether these float switches work by connecting to ground or to +12V when the water level rises and the switch operates?

 Many thanks.