My pressure gage hits 60, and within seconds is back to 40 and the pump clicks on. It lumps fairly quickly bact to 60, off, right away down to 40 and process starts over.

What kind of tank, galvanized pressure or painted bladder?

Please answer Harolds question. What you describe is typical of a water logged pressure tank. If galvanized, you can simply shut the power off to the pump and drain the tank. If bladder style tank, you will need a new tank. The sooner you get this resolved, the less chance for burning up your pump.

It is typical of a waterlogged tank IF it is happening when you are using water. If it happens when water is not being used, then you look at a leaking checkvalve or a major leak in wellpipe, pipe to house, etc.

Completely agree with jlisenbe. But lets cross our fingers and hope that isn't the issue (unless its just a check valve on a jet pump, that would be easier and cheaper to replace than a tank). Work with us Bernard and we will try to help you find the true issue here.