I am so sorry for your loss, FL. I was sending light from work; am so sorry Ozzie didn't make it, but I do believe his spirit is still with you.
As long as we need them, they stay. Especially so, I think, when their death is untimely. For months I would see the kitty, just lurking around the corner.
And my beloved kiwi, a budgie, visited me off and on for years. For months after I lost him, I couldn't concentrate because he was hovering around me and as soon as I was alone, would sing, chirp and fly about. His spirit stayed nearby for years actually, and I could just sit quietly and think of him, and he would show up. When his mate, Mango, died just a couple months later (essentially she committed suicide) she was there with him, although she'd never been close to me.
A baby bird I'd started to raise died after I made a mistake. I had left him in a box under my other bird's cages so he could hear them during the day and not be lonely. I failed to completed lock Benny's cage one morning, and Benny bit the baby on the beak. I knew something was wrong driving home from work, and arrived to find the baby, Cricket, with its beak half torn off. There was no repairing it, so I had to have Cricket euthanized. I was devastated. Crickett stayed with me for a while and I apologized to him. He didn't understand why I blamed myself. He told me (in mental images) the big green bird hurt him. He was very happy to be free and flying, and thought he might get to be born again and flew off.
At the time, I thought my imagination was running overtime, because I didn't think birds could see color. It was years before I learned that they do see color, and I realized that it really was Cricket.
Algiers did not stay, but that was because we did our mourning together while he was still alive. He was ready to leave this plane. However, when he was younger, we communicated all the time. I always knew from home when something was seriously wrong with him...