Prusa i3 improvement - cooling fan
The MKS GEN L v1.0 is a board that according to the information found on the web operates to run on a voltage between 12 - 24 V, this means that all peripherals on the board should match this voltage. A 5 V fan should therefore not be connected.
First, you need to establish that you are using the correct fan port on the board.
Which port to use?
If you take a closer look at the board layout you will find that the top fan connector cannot be controlled, it is a fixed voltage power supply of 12 - 24 V (so basically depending on the power that is supplied to the board).
This can be seen from the board layout:

Or zoomed in on the top left corner:

Note that no pin number is given, this means that it is a constant power supply fan header. A 5 V fan attaching to this port does not seem to be a good solution, it can easily burn out the fan electronics. This fan should match the voltage of the power supply you use, so when powered by a 12 V power supply, attach a 12 V fan or a 24 V fan when the board is powered by 24 V.
As said, this fan port is not controlled by PWM and can therefore not be scheduled from within your slicer, however, it makes an excellent fan for cooling the cold end of the nozzle assembly.
To schedule a fan for print part cooling through the slicer you need to attach the fan to the other fan header below the X stepper driver on the left, if you look closely to the schematics, you see that that is a fan that can be scheduled using the digital pin D9.

Note that this fan also operates at the voltage specified by your power supply; a 5 V fan should not be connected to this port either!
The solution to your problem is to buy a fan of the correct voltage and connect it to the correct fan header.
As you have tried connecting a fan to the lower fan port, and conclude that the fan has never rotated but still rotates when supplied with a correct voltage, you need to ask yourself if this port is:

configured correctly in the firmware, or
not broken.

Now that you know where to connect the fan for print part cooling, connect a fan that matches the power supply voltage.
Why is the fan not working?
The microprocessor of the board schedules and reads various ports or pins based on the firmware it runs. This implies that the setup of the firmware is very important in the use of certain ports. It is therefore important to research if this port:

was meant to be used by the printer manufacturer (so enabled in the firmware)
or board is controlled by which firmware

Once you establish that it is enabled (e.g. the manufacturer describes that the printer has a print part cooling fan), you should try printing a part where you enable the print fan in the slicer software. If not, you need to change the firmware configuration to enable the fan. If this does not work, you should address your attention to why it is not working. A multimeter can be used to read the voltage of the fan MOSFET output or the D9 output. If either one of those doesn't record a voltage, your board or MOSFET are probably broken. To fix this, you could solder an unused pin to the fan MOSFET or a new MOSFET and change the firmware. Another option is to buy a new board and flash a new configuration of a printer firmware onto it.