the silver bullet thing is the ashtray light. Clips into a square hole. The orange wire is the power to the lighter
just go get a cigarette lighter power port. I have one in my Riviera so I can power my GPS. Id tell you yo go to Radio Shack but...
A quick search on Ebay found this- https://www.ebay.com/itm/223248095642 If you want to be slick, you can install it right in place of the lighter element in the ashtray
The part that's still attached to the wire is a fusible link, and they are replaceable. Now it depends if it was snapped off the lighter socket, and it looks like it might have been. So it's supposed to thread into the cigarette lighter socket and then it's pressure clipped to the wire. (some were threaded on that end too). Either way, if you're planning on using that socket as a power source, it'd be a good idea to put that link or something like it back on, that way if whatever appliance or device you have over heats or shorts out, it'll pop and prevent the car from burning down.
The inline fuse is what's attached to the wire. It's not protected further back, it's 12V live. Ask me how I know, I removed the fuses on one car I had and the silly thing shorted out on the steel ashtray frame and caught fire. Oh wait; the power port you're buying has an inline fuse...oops...
