Welcome to our Forum, James!
I've actually done some research on this recently. You can give Ambrosia to any ghost. I had my Sim take a serving of Ambrosia to the cemetary a few times. I laid it on the ground close to where ghosts were hanging around and they quickly started coming for it. I believe they know what it is and what it will do. The funny part was when one would pick it up to eat it, then get distracted by another ghost and start doing that thing where they try to wave off the other ghost, like they're scared or grossed out or something. They would lay the Ambrosia on the ground, wave their arms, then wander off. Another ghost would pick it up and the same thing would happen. Sometimes 3 or 4 ghosts would try to eat it before one was successful. Once eaten, the ghost turns back to flesh and runs off, presumably going home. I did the same thing in my private family cemetary for my legacy family where 9 generations of my Dreamweaver family are buried. One of the ancestors ate the Ambrosia and then walked across the street and into the family mansion. At that moment, she came back under my control! Wow! I wasn't expecting that!
So, yes, you can give Ambrosia to any ghost you see.