I have on my caravan an inline flow control and it needs adjusting now and again so the pump light goes out after the tap/s are turned off. You may just have a system which tells you by the light that current is getting to the pump.
I know yours is the fresh water pump ,the toilet pumps are the same type and my one the impeller was jammed.
Remove the pump and up end it and see if the impeller has jammed, some do because of lime build up if so free it with a small screw driver keep turning until it turns easy then try it again. If still not working check you are getting current to the unit as even if the fuse is still in tacked test there is current in the line pump side, remove it and test yourself or take it to a caravan place and ask them to test it. The other thing to check is the tap micro switches sometimes they could stay on through damp, just a thought try careful with it and on gentle heat, a hair dryer over all taps. These tips came from a caravan repairer when mine went wrong.
Sorry can't be of any more help
Nobby, February 2008