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Here's a pic of the underside of the board.

 

To my eye it looks like they share a common trace on one side, that is most likely a power source, may be 12v it may be 5v who knows. But I am thinking you will see some sort of voltage on that side. The switch should then pass power to the other side it would appear. Just guessing here, you’re going to have to do some testing with a multimeter to see what you get. You could also try jumping across the terminals and see what happens. I would do this after taking your readings to see what you are dealing with. I would assume these boards are fed from a 12v coach supply voltage. Have you checked that you are getting that supply voltage to the board?

Looks like a bit off corrosion on the trace at the bottom, that connection looks a bit suspect.