Letting smoke out of the wires.

The damage should be limited to the oil gauge or there may be no lasting damage at all. It depends upon which one he connected to which stud. If he connected the red to the ground pin for the gauge you may have cooked some insulation on the back of the board or on some wiring as it would have been a dead short through the cluster chassis. How long was it connected? That would determine if it was long enough to burn through wire insulation. If he connected them the other way so that it grounded through the gauge then I'd say the gauge might be toast. Have to test it to know.