One way to get around all these problems is to buy yourself a mechanical capillary gauge. These are generally much more accurate than the electrical gauge and will show a temperature number rather than hot/cold.
I have a Durite gauge that has the 5/8 unf fitting. https://www.ebay.co....p4AAOSwOudZ15od
This you can screw into the block temporarily to get an accurate reading. This will tell you if the car is actually running hot/cold or if you need to replace the sender/wire/gauge.