Get a sharp thin rod (maybe 1/4" diameter) and probe for it where you suspect it might be. That beats digging around with a backhoe.
You may need something like an auger if the ground is hard. You might be able to make a drill by flattening and sharpening the end of a 3/8" rod. It is unlikely that it is more than 2 or 3 ft to the concrete top (but anything is possible). That "drill" can be powered by a standard drill (bigger is better).
You probe pattern should be spaced to ensure that you don't miss the tank. Measure and mark to lay out your search pattern.
After you hit something with the rod you can probe nearby to establish the size and shape of the concrete. When you get a tank-like shape at a uniform depth you have found the tank.