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I did check the gauge function after following the diagnostic check on SM 23-136 and the gauge does move all the way up so the gauge is working properly. The engine is cold and I put a voltmeter on it and it every time I check, I get a different reading anywhere between 104 and 190. Coolant temperature is 65F. Is there something I am doing wrong? Just to make sure I'm not crazy (debatable of course) I tried the old sensor and I get the same readings. They are all over the board between 125 and 197. Is this normal?
When you say ' put a voltmeter on it' I am guessing that in fact you are using a multimeter and that you had it set to measure resistance and those are the values in ohms? If not, that is what you want to be doing. Also, just to make sure, you are measuring the sensor resistance with only the multimeter connected to the sensor?
According to the service manual, the sensor has a highly non linear change in resistance with change in temperature and the lower the temperature the more sensitive the sensor. I expect that at room temperature, just picking up the sensor and holding it in your hot little fingers could cause a significant change in measured resistance. The service manual specifies a resistance of 142 ohms at 56 C. My back of the napkin kind of calculation suggests that closer to room temperature, say non air conditioned 30 C the resistance should probably be around 250 ohms or more. Your measurement of a resistance of between 104 and 190 ohms with a coolant temperature of 65 F seems really odd.
If you have the old sensor out of the car and your multimeter has alligator type clips, connect the multimeter up to the sensor and let it sit so that it comes to what ever the ambient temperature is. That resistance reading should stabilize after a couple of minutes. If the ambient is around 30C, that resistance reading should be around 225 - 250 ohms or more. If it is a lot less, that suggests that the sensors may have a lot of - lets call it uncertainty rather than error - at the lower temperatures. Honda may not care about temperature gauge 'uncertainty' at low temperatures which may explain why the sensor has a much different response rate in the critical temperature range between 85 C and 100C. The acid test for the sensor would probably be to connect it to your multimeter and measure sensor resistance with the sensor suspended in a pot of boiling water. As long as you are not in Denver CO, that water will be at 100 C and you should measure right around 32 ohms (according to the manual). If you have a thermometer, you could suspend it in the pot and let the water cool to 85 C and the resistance should increase to around 49 ohms. If the hot water test gives you those results on the sensor, the sensor is probably as good as it is going to get.
Honda does not provide a calibration test for the dash gauge. However, if you want to test the operation of the gauge, I suggest the following. Go to Digikey or some similar electronics vendor and purchase a 50 ohm and 30 ohm resistor. Digikey lists about 100 million resistors, you want a through hole style with a 1% (or better) precision with 1 - 3 watt rating. Something like this:
https://www.digikey.ca/product-detail/en/riedon/UB3C-50RF1/696-1043-ND/2176599
If you are anal, you can buy a 32 ohm and 49 ohm resistor; but, those tend to be oddities and you will need to order a minimum of 1000 to get them. For testing, I think the 50 ohm and 30 ohm should be just fine. Connect the 50 ohm resistor between the gauge sensor wire and a good ground. Switch the ignition to on and the temperature gauge should be reading the equivalent of around 84 C which is probably slightly below normal. Turn everything off and replace with the 30 ohm resistor. Switch the ignition on and the temperature gauge should be giving you a temperature reading equivalent to around 101 C which I am going to guess should be approaching the panic mode. For interest, you could purchase an additional 40 ohm resistor and I am thinking that this should probably put you in the above comfort but not panic mode on the dash gauge.
If the dash gauge tests out OK with those resistors and the sensor passes the boiling water test, that is probably as good as it gets with the OEM parts. Something to note is that in the normal operating temperature range, the sensor and the gauge have a sensitivity of somewhere around 1 C / 1 ohm. The result is that if you have a bad electrical connection at the sender (or anywhere), it can cause a material error in what the gauge displays in its 'normal' range. Make sure the connections are clean and you may want to try applying something like Ox Gard to the terminal to improve the connection