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I think you meant to say they are on the same circuit?
No sir, in my truck the cig lighter and the obd port are on the same circuit and the power point is on a separate circuit. I would suggest checking fuse #3 under the dash. Should be a 20 amp fuse in the slot.
Also check pcm power. The pcm relay and fuse. Came into that problem when my gem went bad the connectors on the back side of the pcm relay weren't connected.