When i run water from my deep well pressure tank system, the pump kicks on and off every 1-2 seconds the whole time the water is running. Pressure is good, but a very pronounced surge that wasn't there a few months ago.

What type of well tank do you have?

If you have a bladder tank, the bladder has a leak or has ruptured. You need to replace tank.

If you have a galvanized pressure tank, the tank is water logged. Drain the system down by turning the pump off, open a faucet and open the drain line. Let tank drain completely, close drain valve and faucet and turn pump on.

One more point. If you have a bladder tank, and you probably do, then you can still drain the tank, add five or ten pounds of pressure at the air valve on top of the tank, then turn it back on. That will get you by for several weeks until you can put on a new tank. That will also verify that you have a waterlogged tank if it causes the short-cycling to stop.