Gauges Die w/ Headlights On.

^^YES. Add a pigtail ground wire from the cluster somewhere to the dash frame. "For now" try loosening/ tightening the cluster mount screws

..........EDIT........Are you saying the gauges actually quit, or that the LAMPS for the gauges go out?

The dash lighting is a little bit of a trick

The headlight switch has TWO power sources, one for only the headlights.......and the other comes from the tail fuse, and powers tail, park, and dash lamps.

That power goes through the switch, through and OUT the dimmer control AND THEN goes down to the INST fuse on a tan wire, through that fuse, and out to the dash lighting on ORANGE wiring.

You need to check both ends of that fuse, with a meter, WITH the park lights on, and while manipulating the dimmer control. You should have varying voltage there.

Do the "non cluster" lamps work, like, radio, heater bezel, etc?

Could again, be cluster grounding, dirty / corrosion at the sockets / PC board and of course the lamps themselves