First. Light out means it's not the fuse at the pump.
Question about those switches. are they ON/OFF toggles or are their three position spring loaded return to center momentary switches that feed signals to a control board somewhere..... Yup.
On my RV there were two 3-way switches (SPDT) and if no electronics between battery and pump.. just Fuse----Switch======Switch----Pump
(The two wires between the switches if both switches select the same wire pump is on. they are called 3-way because they have 3 connectors on the switch)
But another system is Fuse----Control board---pump
And a whole bunch of switches to the control board.. I've not seen one. but read about it.