you can use cigarette lighter style PSU, or something like this. any 12+ Watt 12-24VDC PSU will do.
it is just as small and it has adapter with screw TB to make wiring easier.

 

The tag on the motor identifies it as a brushless motor, further marked as powered by 12 or 24 volts DC. BUT now we have a description of the speed control signal as being from zero to 5 volts. We really do not know the speed control input resistance, and that will affact the resistor values for the speed control.
So now we have a question: is the TS capable of adding the speed control hardware.

 

Thank you for all your comments and suggestion! Realizing that this might be more complicated and way above my current skills lol I will consult the uni technicians for their help and the original supplier. Will let you know how they set this up!

 

Hello, just got a reply from the original manufacturer. Two possible configurations can be done:

1. The red and black wire can be connected to power supply, while the white and green wires can be connected to another 5V power supply. This way, the pump runs at full speed.

2. The red+white wires can be connected to one end of the power and the black to the other end. The green wire can be left unconnected.

Thanks again for everyone’s help!

 

Since the apparent requirement is for variable speed operation, it gets a bit more complex in that a variable voltage is required for the speed control.
The green wire would be left not connected, the speed control white wire will go to the wiper of a potentiometer, probably 5000 ohms. the red wire will connect to the positive 12 volt supply, The black wire will connect to the negative terminal of the 12 volt supply. In addition, one end of the potentiometer will also connect to that same negative point. The other end of the potentiometer will connect to a resistor of the same value as the pot resistance, with the other side of the pot connecting to the positive 12 volt supply terminal.
This arrangement will allow the speed control white wire voltage to vary from zero to about six volts, which should allow the speed to vary thru the whole range.
Since we have no hint of the timer requirements, no advice about that aspect. BUT the timer will need to be in the 12 volt supply circuit, to remove all power after the set time interval.