Red and black are the 12V supply wires from the cassette area (where the fuse and reed switch are located ) and the brown and blue wires with in the inline crimps on them should go to the pump inside the tank . The fact that they have the red crimp connectors on them shows the pump has been changed previously .Once you press the pcb mounted switch ,those two wires should have 12V between them. If you connect a pump and it fails to run then two things may cause this
1. the PCB is faulty - faulty switch or the circuit is U/S - which looking at an image of your pcb is highly unlikely as it looks in good condition as does the switch and switching transistor.
2. the voltage coming into the pcb on the red and black wires drops when under load , which can be cause by corrosion somewhere in the wires or the fuse pcb .In the attached photo the red arrow shows the supply wires, the black the pump output wires and the green the cassette full reed switch to the PCB mounted LED. Its a bit fiddly but if you can connect your multimeter to the red and black wires whilst connected to the pcb and with a pump also connected then when you press the flush switch on the pcb if the voltage drops ( say to 9v or less) you have a bad connection somewhere in the supply wires, iF it stays around 12V or around that the supply is OK retest on the pump wires (with a pump connected) , if that voltage doesn't reach about 11V then the short wires/crimps connectors are faulty.
As an aside as your PCB is a later version than the one have images of could you please take another photo of the component side (similar to your posted image ending 57D8) with a better focus of the board and the components.