Plugs like that are usually molded single piece items, the wires are fitted by having a springy tab sticking out of the connector end of the wire. As the connector end is pushed into the plastic plug the tabs spring out and grip the plastic, preventing it from coming back out. You can remove them again if you can identify where they are and push a fine flat bladed screwdriver down the back (where the wire goes in) of the plug, aiming to fold the spring tab flat so it is no longer against the plastic
Take a look at this picture of a molex connector in component form, for a better idea of what I mean:
This picture features 4 connectors (two male pins, two female pins) and is intended to allow 2 wires to be connected and disconnected. The connectors are paired up for shipping but in use would be detached from the metal bar that has a rectangle and two circular holes in. They would then be crimped onto the end of a wire, and then those two small metal pins sticking-out (creating a Y shape) are the tabs that hold the connector into the plastic block. Removing this connector from the block again requires the pins to be folded flat against the body of the connector, the connector slid out, and then the pins folding out so they will grip when reinserted
All that said, I strongly recommend you consider replacing your entire plug and socket with something that IS available in your country. The plug you've pictured SHOULD be available as it will have been used on countless different makes and models of car. See if it has any manufacturer name on (not necessarily the brand of your car)
I'm not entirely sure why you're posting on lifehacks, as you've just added information to your question that seems to imply that anyone jury-rigging any kind of thing that is not an original car part as approved by the manufacturer will instantly void their insurance (yet you've also commented to imply that a home-made repair has been carried out on your car before - confusing; have you been driving uninsured all this time)..
That said, when i recommended "making a plug" - spray the socket full of some lubricant, attach two individual wire spade connectors to the ends of the wires, then push them onto the pins inside the socket, fill the entire socket with silicone sealant (like what you put round your bath) and let it set - you'll now have a new plug, molded to the shape of the old, with two connected non-shorted wires embedded in the cured silicone. Old socket, new plug. The lubricant spray should stop the silicone sticking to the socket for easier removal