The connector with two wires is for the vehicle security system LED that is built into the base of the stock rear view mirror.
The other connector should be flat a 7 pin connector, however only 3 wires are actually used. There is one wire sort've over by itself in cavity #2 of the connector, it is probably black with a dark blue stripe. That is the power source for the reading lamps. Two other wires are on the far end of the connector, in cavities #6 and #7. The one in #6 (probably black with a brown stripe) is the power for the courtesy lights. The one in #7 (probably black) is the ground. So, for your purposes, it sounds like you should be probing between #6 (positive) and #7 (negative).
I believe the reading lamps power source will have voltage on it all of the time, but the courtesy light power source is controlled by the body control module (BCM), and should only have power when the interior lights should be on. There is a delay function in the BCM which will leave the lights on for a certain time after the door is closed and fade them out gradually. Usually this fade out happens pretty much right after the door is closed, however I have had the lights remain on for 30 seconds after the door was closed. (I'm not sure what triggers the longer length of time.) So, its possible to have power on the courtesy lamp circuit for a while after the door is closed - that may be why both wires showed power when you probed them. (The BCM appears to have only one courtesy lamp driver circuit however, so if the other interior lights are off, there should be no power to the courtesy lamp driver wire running to the rear view mirror either.)
Anyway, with the above info in mind, you may want to re-probe those wires to double check that. If the courtesy lamp wire has power even if the other interior lights have gone out, its possible the previous owner altered the factory wiring more than they let on. The wiring from the mirror runs to a connector under the dash which then goes to the BCM, so if your probing shows that the courtesy lamp wire has power all the time, it might be necessary to trace it back and find out what has been altered.
Did the original owner re-install the factory mirror or do you have something aftermarket now? If its the factory mirror, it may be as simple as the bulbs being burnt out?
I hope that helps!