Hello and welcome to JustAnswer!
You are just having problems with the illumination of the instrument cluster correct, the gauges all still work fine?
Do you have a voltmeter or test light to do some simple electrical testing?
Excellent. I'm tied up at work this afternoon (I'm a full time tech). I'll get some testing information to you this afternoon as soon as I get a chance!
Ok. When the lights go out you'll have to remove the instrument cluster to access the connector on the back side. Once you get there, check for power on the orange wire in pin 12 of the connector. Also check for ground on the black/orange wire in pin 11 right next to it. You are looking for less than 5 ohms to ground on that wire, perfect continuity being ideal.
Let me know what you see and we'll go from there. The fact that they don't come back on until the car is restarted makes me hesitant to be swayed either way at this point between body controller or instrument cluster. Wiring is also a possibility too. We'll get it figured out!
No, it's not a common problem on these. Instrument cluster lighting is controlled directly by the body controller. There isn't a relay to power the circuit, and it's not controlled by the switch. There is a possibility of three things that could happen.
The BCM may stop driving the lights because of an internal issue in the BCM. It would need to be replaced if that's the case.
If the wire from the BCM to the cluster shorts to ground the BCM may disable the lights to preserve itself from damage. This would likely keep the lights off for a period before the BCM decided to try powering the lights again.
The last possibility would be a problem on the instrument cluster's circuit board. If there is an intermittent open circuit between the electrical connector and the illumination bulbs it will take the lights down.
It will require removing the instrument cluster to diagnose it while it's happening. It isn't a major job, but will require some dash trim panel removal to get the cluster out.