You keep the timer coil energised at all times. As long as you keep power on it, it will keep "flashing" on and off at whatever interval you set.
If you need to restart during the off cycle, you just need to momentarily drop power to the timer coil - when power is restored it will begin flashing again, starting with the "on" flash.
See attached. K1 is just a simple relay that creates a start-stop circuit. The stop button will stop everything. The start button (which I forgot to label) has a NO contact to bring in the start-stop circuit, and a NC contact to break power to the timer coil when pressed.
You press the start button, K1 comes in. You release the start button, T1 is powered up, which energises K2 (pump contactor). If you press the start button again, the pump will restart as soon as you release it. If you press the stop button, everything stops.