Unless you can verify that the switches mounted on that board are completely disconnected from every component on that board you are going nowhere.
One of the first things to do when tracing a problem, no matter how simple the circuit, is to eliminate every unknown, that board is an unknown.
Either find two simple bare switches and try the circuit or remove the wires from the board and leave them disconnected and not touching.
That is now the state with two switches in the off position, measure the voltage.
Join the wires that went to one switch together (switch closed) and measure the voltage, disconnect them and do the same test with the other two wires. Now compare the results