Needles in gauges just peg out

There are two possible reasons I can think of:
- both sender leads are short circuited to ground (unlikely, but possible)
- the instrument voltage limiter has failed (more likely)

If the car does not have an oil pressure gauge, I'd consider replacing the limiter, which is a separate component plugged into the instrument cluster printed circuit board. You can test the limiter by connecting a voltmeter between the connector for the temperature sender and ground. The voltage should constantly fluctuate between 12 volts and 0.