Is your well something like this originally, and installed an electric pump to have water pressurized in pipes/hose?When it rains we get the well back. It is an old shallow well that goes dry when the creek dries up. When the monsoon comes, it works again! But no rain for a few days, and it dries up again. We got an hour of lawn watering yesterday before it quit.
Asking, because just wondering if you would be able to dig deeper to reach water-shelf during the times your water runs out .
I, as a small snipe remember we had such a well,(rural area) until I was 8 years old. Then family moved into city. (Chicago)