The wire end points are interactive, the target points are apparently just incredibly finicky and inconsistent. With enough tries though, you might get it. But if you do, you later get the ability to repair lights by assembling a puzzle.
If you get to that point, I recommend not playing on a laptop. Not because the trackpad makes it harder to solve, but because it's a lot less tempting to throw a desktop across the room.
Dear dev: Not a bad game concept, but please fix the click/drop/whatever detection. In the headlight repair "minigame" the light might be the least broken thing.