Could be lots of stuff.. ground water to poor sloping around the house....

You have a couple more options on trying to evaluate if a tank is present.  1) If the property is old, you may be able to identify the presence of a tank on a sanborn map that you could correlate with the anomaly in the field.   2) use a utility probe rod or a hand auger to dig down to the tank and see if its there. 3) review old site plans to determine the presence of a tank4) will the bank allow you to just collect soil and/or groundwater samples adjacent to the tank in lieu of digging it up? 

I am just finishing up installing a completely new system including new ductwork ( old was in floor and had long term groundwater problems ) in a 1380 ft' house .

It likely is a ground water pressure problem.

In December 2016, after we just got done drywalling the entire basement, it flooded due to ground water rising.  

Otherwise, major liability if someone gets sick, or it leaks and contaminates another property or worse, groundwater.

Some areas on ground water have toxic levels of Aresnic and if a Tenant ever decides to sue could own your property.

It supposedly is taking in under ground water?

Also, if another peril (cause of loss), such as wind. causes damage that allows the water in (ie. wind blows roof off so raing damages the interior) then there could be coverage.Any ground water that seeps in, surface water that gets in or damages the structure, or similar are normally insured with a Flood Insurance policy.

The property is/has:7 acre cave20-30 foot ceilingsVehicle accessible (can even take a tractor trailer through it)2 acres in front of the cave that have been cleared and are along a roadMillions of gallons of groundwater (I'm talking enough to canoe on)Located in a medium sized city near a metropolitan areaIf anyone has any suggestions, or would like to know more information, please don't hesitate to message me.