Temperature gauge being erratic
 

I have a 2007 Mountaineer with 95,500 miles. It has been sitting for 4 years due to my wife not wanting to title it. I kept the battery charged and drove it occasionally on my road. Finally, my wife let me put it back on the road. So, I am expecting problems and issues. The first problem is an erratic temperature gauge. It was overheating so I changed the thermostat. But it is still behaving erratically and doesn't smell like it is overheating nor does it leak any antifreeze and the coolant looks clean and full. I can give it gas and it will go back to cold. Does anyone know where the coolant sending unit plugs is? I want to check the terminals to see if they are corroded. Also, there is a P0117 code showing
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Update: It overheated. The temperature gauge was showing cold but steam was coming out of the radiator cap. Top hose was spongy. There was nothing leaking underneath. Either the water pump is not working or the radiator is plugged up. It’s a new thermostat. It also started running rough before I shut it off. All hoses were good. Where should I go from here?