Since you stated you had other electrical problems I am not sure this will help but, other than 12V itself you have two other factors to allow the pump to work. One is the pressure switch which is most likely built into the pump. The other is a latching relay which would give you the lights on the switches and also power the pump. Not sure where yours is located but I would start by looking at the pump and try to follow the wires back. My guess is it would be somewhere near the pump and you could try to jumper around it for a test.
Brian, Loretta & Daisy (Golden Retriever)
2008 Holiday Rambler Endeavor 40 PDQ , ISL 400
2014 Ford Explorer toad