Engine Temp. Gauge Issues

Any chance the fuel gauge is also reading a bit high? If so it's likely the regulator called by several names, IVR, instrument limiter, etc. On a non-ralleye dash it plugs into the circuit board. I'd look around and get a modern solid state replacement. Online outfit called RTE is one good one

You can test the gauge system for accuracy by sustituting known resistors for the sender Here is a doctored photo of one type test box, showing the resistors. They are the same for all three gauges (oil if you have one/ ralley)

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Another way you could go about this is to let the engine warm up to exact middle of scale, then quickly disconnect gauge sender wire and measure sender resistance and see if it is close to what is listed above, 23 ohms for mid scale
Thanks for the guidance. The fuel gauge is correct. The gauge is pegging it is reading high. Does go up slowly then reads high.