Submersible water pump
You need to have a submersible pump submersed when testing. Most deep well pumps ALSO need adequate back pressure to limit the current they draw (normally provided by that long pipe up the well to the surface.)

Running dry is bad for all submersible pumps, and "in a bucket" (i.e. with no output restriction when outside of the well, or without adequate head in a well) is bad for most. They expect to be in water (generally near 10C/50F) when operating, and that water serves as lubricant and coolant. 

Your on/off cycling is probably caused by the pump's protective circuitry shutting it down due to overheating.