I have this same pump at work so I know what you are talking about. Easy way is to use a relay, specifically a DPST relay, apply 12v to the common pin, connect the NC pin to the pump, the no can be left floating, connect the coil to the arduino (ideally via something to isolate the inputs on the arduino from the back emf). When arduino is connected and the coil is activated no 12v, pump runs. disconnect arduino the relay goes off and supplies 12v to the pump, pump turns off. Additionally, if you dint activate the coil, the pump remains off. Sorry for any typos or what not, sent using my phone.
Thanks Pedro,I am sure that with a NPN or a delay it will work, but following the instrument guide it should work with a TTL signal. Which is much more simple. In fact it works perfectly with the direct connexion to a digital Output of the Arduino, but the unique problem is that of been ON when port output is LOW, even when the Arduino is disconnected.I am sorry but I do not know what is a Pullup Resistor.