radio w/ headlights?

The PO of my 94 jeep cherokee has apparently done some unique wiring.  I have an electrical FSM for the vehicle but am not sure where to start or what to look for, this will be my first try with electricl issues.

If I pull the headlight swich on with the jeep off the radio will come on also; if i dim the dash lights by turning the headlight switch while driving the radio will go off. The cig lighter, rear defroster, and highbeams are also not working and all appear to be on the same circuit. Where should I start? and what should I lookk for?

Does the clock work (ie retain the correct time)? 

I would start with the red wire on the radio.  Verify that it is 0vdc when the car is off (regardless of headlights) and 12vdc when the ignition is on (regardless of headlights).  I would then make sure the ground is grounded to a solid ground.

One of the first radios I ever put it I hooked the ground to the dimmer wire - it measured ground with the headlights off.  Well, later that night I got a call that the radio shuts off when the headlights are turned on - I had ground the radio to the dimmer circuit.

Yes the clock stays on (doesnt reset when jeep is turned off). I was looking at the wires and if I remember the ground from the radio was connected to an orange wire, which is listed in the diagram as the dimmer wire. So I will start there tomorrow (at work now) and post back what i find. I ASSume it should be connected to the black ground wire. I am waiting on a factory radio to arrive so I can put it back to stock so I will better starting point.

Could that ground connected to the dimmer also cause the other options to not work since they are the same circuit? or would that be caused by something else? Jim