First check the inside of the bulb holder for corrosion and damage. If the bulb isn't a tight fit/making contact, the electrical circuit won't be complete.
It's more likely to be a simple wiring problem- an earthing problem.
Check the wire on the defective light - particularly the black earth wire for corrosion/security of attachment. If the bulb can't 'earth' it won't light up.
A quick check you can do is put the bulb into the holder, switch on the lights, then hold a wire against the metal side of the bulb with the other end of the wire against any suitable earthing point.
If the bulb lights up - it's an earthing problem.
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