Engine Running Hot / Gauge Issues??

Going from "N" to "R/M" in a couple of seconds is not good and can't happen with a correctly functioning system. I believe either the gauge or the sensor (CTS - Coolant Temperature Sender) are bad. You could also have a bad connection between the CTS and its plug. The CTS is on the lower intake, just to the right of the distributor. It looks like a brass plug wit a single 90* plug on it. If you look inside the plug, you'll see two pieces inside. Try to squeeze them together some more, and you might try some electrical contact cleaner. See if that affects the gauge any.

If you have a code reader that can read PIDs (engine sensors), you can read what the coolant tem that the computer sees. This comes from the ECT (Engine Coolant Temp Sender), which is screwed into the metal heater lines on the passenger side of the engine. If the ECT is giving the wrong readings, the computer will not know the engine temperature and add more fuel to bring the engine to operating temp. This usually results in an engine overheating or running really hot.