On searching for suitable component to control the DC motors, I found that a L293D would be suitable. And on searching for a L293, to my surprise, it's available as an auto-complete keyword! Why is that?
I remember that it's what I bought for fixing my Nexstar mount. The mount dies after the operation, but I still got one such chip unused. Now, I know what's a H driver, and after reading the data sheet, I believe it's going to be useful for my project.
So, I setup the circuit, but the motor couldn't be driven according to my understanding. (*) I believe output clamp diodes are really needed for inductive transient suppression.
For simplicity, I believe that I'll eventually go for a setup of four SPDT relays. I believe this will be the basis for the autoguiding signal control, as well as the hand paddle that I'm going to build. I found a fan remote control having four keys originally, but then I have thrown away one of the covers already, what a pity!!!
(*) Additional remarks on 2nd of Jan:-
I've conducted another test, this time, I set 2A to GND, last time which I left it open. The behavior of the chip is now as expected, but this time, I just use a multimeter across the output 1Y and 2Y instead of a motor, but I guess even if a motor is placed there, it shall work.
But today, I've placed an order of a motor controller kit based on L298 which should be even more powerful, let's see. At the time being, maybe I will try out L293DNE first? Anyway, it's going to be interesting, I believe.
At least I've learnt something through the process and it's definitely funny!