Hi,
To confirm the controller is most probably at fault, use your multimeter to test if the reverse (Brown) wire goes up and down when the reverse switch is activated.
To do so, connect your DVM to ground at the controller and to the brown wire at the controller. Set the DVM to Volts DC. Apply power to the system and note what the voltage is. My guess is it will be something around 4.5 VDC. Flip the reverse switch and the voltage should drop to something around 0, and should return to the hi reading when the switch is returned to normal . (Obviously the readings could be just the other way around). If the pin goes up and down, the problem would seem to be localized to the controller.
TTFN,
Dennis