Temp gauge problem goes to red when key is on. Engine off?

[e30m20TurbO7]

So when I turn the key on the temp gauge just goes all the way to the red even when the engine is off. If I turn the key off and I hit the gauge it goes back to blue. Is power going to the gauge ? When the key is on?
I had a wire short in my engine harness a month ago that went to the relay because I had a cap off the relay to test to see if it was working and it arched it self on the body burning up a wire to constant power in the harness, this is a e36 harness obd1 m52 swap. The temp gauge worked fine before I burned up a wire.
I fixed the wire going to the relay and noticed the temp gauge was doing this after. If I unplug the connector from the temp sensor there is no change the gauge just goes to red when the key is on.
Does it mean it has low voltage of to much resistance ?
Where do I start ?
Cluster ?
Sensor ?
Si board ?
C101?
Confused on what to do

[dnguyen1963]

Take out the cluster and look at all the solder traces, especially the one leading to the temp gauge. I would not be surprised if you see you burnt traces.

[jlevie]

That sounds like a short in the wiring between the gauge and sensor.

[e30m20TurbO7]

If the mother board on the cluster has burnt traces on the side that doesn't show the motor board is the short in the cluster ?

Take out the cluster and look at all the solder traces, especially the one leading to the temp gauge. I would not be surprised if you see you burnt traces.

[dnguyen1963]

If the mother board on the cluster has burnt traces on the side that doesn't show the motor board is the short in the cluster ?

A burnt trace means that the electrical current cannot reach its intended target. You have to trace it to the end to see which component is the endpoint. Take a pic and let me look at it if you have doubts. A short elsewhere can cause a surge and burn the solder trace.