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An 11 volt source should provide sufficient voltage to make the bulb workable if not at full efficiency. However, the path to ground (after the load) must be complete for current to flow back to the battery and allow the load (bulb) to operate.
Assuming source voltage is available at the bulb socket contact and the bulb is good, attach a test wire from the ground circuit at the bulb holder to a clean metal ground path to confirm a working current path up to that point. If not, the normal harnessed ground path is compromised (open circuit or thereabouts). The typical malfunction is the bulb, but an open can be anywhere between the last source signal and the ground path.
One does not need a working bulb (or load) to identify source voltage which is an independent element of a circuit.
Sherwood
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