Diagram of the controllerThis is the controller. The left part is an LM317 with two resistors calculated to give 3.15V which was exactly what was supplied from the PCB I removed from the timer. The formula for the setting is: Vout = 1.25 * ( 1 + R2/R3) = 1.25 * ( 1 + 330 / 220 ) = 3,125V
It took me about 2 hours and a lot of tests to find out that the output of the timer is not simply giving 0.7V like I measured but actually sinking to ground when the status is set to off.
The resistor in the base of the transistor is calculated to create 240µA in the base so the amplified current will be more then 100mA which is the maximum a BC547C can drive. The motor will only consume about 30mA so that is more then enough. I have included a diode to absorb the reflow then motor may cause when the power is removed.