soldering wires to 12 V car plugs?
Sure. You can twist the appropriate leads together and solder them. Be sure to heat shrink or tape the connections afterwards to prevent shorts.

Or use a block terminal. Or crimp. It’s up to you. All of these would hold fine if done right.

edit per new image First remove the metal parts from the plastic case. Apply flux. Solder your leads directly to the surface. Clean flux residue. Reinsert the parts back to the plastic case.

Note there is a small pre-drilled hole where your negative lead should be inserted before soldering. Make sure your solder flows through and plugs the hole.