I love a Mach 1
You may have a short in the wire that makes the light come on. If you can find a wiring diagram, find the wire that makes the light come on and test it. Also check fuses and you may want to check the actual bulb on the dome light, because if I'm not mistaken, the bulb that lights up when the door is opened is different than the ones you turn on with the switches.
So you have a few options for solving this:
1. Check the center bulb in the dome light housing.
2. Check the fuses
3. Check the wires for shorts
Since it happens with both doors, it's more than likely the bulb itself. I could be wrong, but I tried.