If the battery pack is producing what sounds like a hum, one should put their hand to the battery to see if it is vibrating. If the battery is vibrating even slightly, the hum sound may be caused by relay chatter on the inside. If a relay is changing state rapidly, check the wiring of your fixture and disconnect power going to the battery and the AC ballast (do this by the circuit breaker or equivalent, not using the test switch). If the noise/vibration does not cease, replace the battery.
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