Sorry im abroad and cant draw the schematic. The connector has one 12V pin, two GND and two 5v.
Yep, the pump works when the RTC randomly gives the right hour. The pump is directly connected to the 12V of the supply, and GND is controlled with the TIP120.
Everything works fine and is right connected, again the only problem is the RTC, giving only the right value when the UNO is powered via USB.
Ive already tried powering it with the 5V (supply) - 5V pin; 12V (supply) - Vin pin; 12V jack of the UNO; and even connected via USB a step down converter to turn the 12V from the supply to 5V.