What you want to do is to lift the well cap and take pictures of what you see (use a camera if you have one) including at the depth of the pitless if possible. Also search for the word pitless and try to match what you find with what you see. And hear. With the cap off, you should hear that water flow loudly coming from the casing. You can move the power wires gently to improve your view. Put the cap back on before leaving the well.
Actually, this is probably time to call your well pro, who's sticker is probably on or near the pressure tank. That one will already know what kind of pitless you have and will be able to pull up your well pipes and make the repair.
Edit... OK... saw your update. There will be an O-ring or similar gasket there, which may have failed. I am surprised that the leak of a failed seal would pass enough water to make the pump run continuously, but there it is. The well company can pull the drop pipe up a several feet and make the repair. It is possible they will have to change the pitless, so leave your excavation open until the repair. Most likely they will not have to change the pitless but just the gasket. Or it could be a pipe failed enough to spew water where it attaches to the pitless.