What would cause a Spur Switch light to go off when the device is turned on?
Assuming the light itself isn't bad, then the combination of a dim light and the dishwasher making it go out sounds like a break in a wire or a corroded connection. A break or corrosion can allow enough current to pass to light the bulb dimly, but when a higher current is called for the resistance of the break or corrosion goes up, causing an apparent total failure.

See https://diy.stackexchange.com/a/27285/82