Looks like either a female spade connector or a mini capless bulb holder and that metal tang looks like an earth to the lighter body so I go along with the cigarette lighter illumination.
Nope, I have checked the back of the ashtray and there is only one 3 pin connector so this wire must be for something else. Somebody must know!!! I guess at some point it may have had a different ashtray with a different connector but v. unlikely. It's bugging me now.
Nope - it is for something. I checked the voltage. Weirdly, it is around 0.4v with no ignition and about 0.9v with ignition on. I'm going to get to the bottom of this one with someone's help!!