Eddie,

I'm not sure I understand you correctly. If you have "apparent" groundwater, the water level should be at similar depths at different holes around your pond. The "squishy area" may very well be a contact spring. Remember, you can have several things going on, one above the other.

You referred to hitting a layer of gravel and seeing the water level rise overnight but not seeing water in "the rest of the 4' sections of the hole". Do you mean that the water rose higher than the bottom of the other adjacent holes that didn't penetrate into the gravel or that the other holes just weren't deep enough to intercept the water? If the former, the water in the gravel may be under "head" due to an inclined orientation and an overlying clayey or confining layer.

I think you are on the right track in digging a few holes around the perimeter of the pond and letting the water come to equilibrium for a few days. If you can get access to a hand auger and a few extensions, you can bore a hole, drop in a piece of pvc pipe, add a little gravel around the bottom, and backfill the hole around the pipe back to the surface to make a rough version of a piezometer. Open holes can fill w/ rainwater and seal due to siltation giving the impression of having groundwater when there is none. Just be aware of going thru layers of clay and into something like sand and gravel. In that case you'd want a hole into but not thru the clay and a separate hole thru the clay and into the gravel (nested piezometers). Depending on what you see, you could be looking at perched groundwater above the clay, water in the gravel under artesian pressure, or both. Is there much relief in your area or is it relatively flat?