I just open the controller box, actually, it's not anything special because you will have to open it to replace the battery inside, which is a 9V alkaline, I found the expiry date of the battery is like 2006, so I know this focusing motor is very energy efficient!
Back to the topic, I found that controller is surprisingly simple. It's basically to provide DC to the motor directly from the battery, with a simple resistor in serial, and also a variable resistor, which is just to control the speed of the motor. The two (directional) buttons do the job about swapping the polarity of the DC to the motor.
I'm sure the motor inside the focuser is just a DC geared motor. So, my direction is correct to find similar offering. That is, a small DC geared motor having low RPM, and then I will have to build a controller box similar to this focuser controller box, but it will have two ports, one for RA and one for DEC.
And then to add a ST-4 like autoguiding port there.