Alternator Wire/Tail Lights

[nolafishr]

I am having an issue with my 93, I noticed a wire I forgot to hook up from the alternator, it is a single black wire and looks like a ground wire, can anyone tell me for sure and does it ground on the engine block? I also noticed that my tail lights are staying on and I do not have the lights on, I noticed this after I removed my battery to put some rubber material for it to sit on and hooked the battery back up, would the tail lights go out when I hook the ground wire back up on the alternator? I never had this issue until I did this.