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The signal for the third brake like or "high-mounted stop lamp" (terminology from the FSM) is the same source as the rear brake lights - the stop lamp switch.
If you're getting voltage at the rear brake lights, but nothing at the harness for the third brake light, then there must be some break somewhere along the way.
Found the issue last night. Playing with the wire & connection while the daughter stood on the brakes produced a glowing red 3rd brake light. My initial thought is the connector clip to the light - something obviously is loose.