Most all thermal switches, couplers and sensors work by going to ground gradually. The warmer they are the better the flow of current to ground.

That translates into a reading on the gauge. A fast jump to to full temp or gauge travel means it is grounding in the line (Wire) proir to getting to the sensor. Look for a bare spot on the wire in route to the sensor. This will most often be found while passing thru a metal plate such as the firewall. However most manufacturers have learned that lesson and pass it thru on a coupler to prevent this. Many manufacturers put a heavy sheath on the thermal couple wire to protect from chafeing problems. Also look for the looms and supports that guide the wire to the sensor, has it chafed into the wire?

I have found other wires or metal chafeing on the back of unprotected instrument cluster circuit membrains. I do not know if this applied to your vehicle. Does it have a film style or actual circuit board that is exposed on the back of the gauges? If so is anything touching against it? Was work done in the instrument panel, stereo or other systems behind the dash.

I have found some gauges that jump full over if they loose all connection to ground. Test this by unplugging the connector to the sending unit and turn on the key. If it jumps all the way you are looseing your connection. This is not as common. Then see if the connections are all tight, for a cause!

A instrument cluster with a poor ground on the system will also have the instrument lights dimming and blinking brite, dim, etc. The ground is common to all of the group.

The last is a shorting connection or wire in the instrument coil inside of the gauge.

Last question, any oil drips coming from under the dash above your feet?