Factory Gauges & senders

OK, The connector that goes on the oil sender did have a insulator on it once upon a time. Many here can say they have never seen one of those insulators. The heat there causes them to crack and fall off.
When that bare wire terminal lays against any metal ground source it pegs and cooks that gauge.
If the other 2 gauges work you can know the limiter is working and the above senerio is very likely the case.

Just for the sake of edumakation... The OEM mecanical limiter and some of the aftermarket solid state regulators can and will send full system voltage through a gauge in a shorted state. The gauge can live only 3 to 5 minutes in this condition.
At a fixed 5 volts and 1.5 amps a gauge winding will live approx 15 minutes depending on its age/condition.

Hope this helps