While this happened when I was very young, I don't believe it was the product of a little boy's vivid imagination due to the facts that the phenomenon repeated itself many times, and I didn't think it was a ghost.
When I was about four, my family moved back to the US for a few months before relocating overseas again. We stayed in my grandmother's house, and as my father had already begun work at his new job abroad, it was only me, my brother (two years older), and my mother staying with my grandmother.
We all slept on the second floor of the house. The staircase to access the second floor was along the northern wall of the house. At the very top of the staircase, in the northwestern corner, was the bathroom. If you were walking up the stairs, as you reached the second floor there was a large area on your left onto which all the rooms on the second floor opened. The bedroom my brother and I were sleeping in was in the southwest corner of the house, and my mother and grandmother were sleeping in the same bed in a room just next to ours, on the southeast corner of the house.
Each morning, I would wake up just before dawn, when it was still very dark but just beginning to lighten. I would go into my mother and grandmother's room and crawl into bed with them. From where I would lie in their bed, I could see across the second floor to the staircase from the first floor.
One morning, I saw a cloudy, shadowy figure come up the stairs, turn left, walk diagonally across the space at the top of the stairs to the door of my mother and grandmother's room (where I was lying in bed with them), and disappear. I distinctly remember seeing first the head of the cloudy figure, then the torso, then the rest of it as it came up the stairs and into view.
This happened every morning for a few weeks. I didn't know what it was, and I began to think of it as the Sandman. I tried to see whether it threw sand in our room when it came to the door before it disappeared, and wondered why it didn't throw sand in the room my brother was sleeping in, too.
One morning after I crawled into their bed, I really had to go to the bathroom badly. I was waiting for the Sandman, and I didn't know whether I should wait until after he had come and disappeared or try to go before. I saw the cloudy figure come up the stairs, turn left and begin to walk towards our bedroom door. For some reason I'll never understand, I decided to climb out of bed when it was about halfway to our door. I was staring straight at it. As I climbed out of bed, it stopped moving right where it was. Still staring straight at its head (I couldn't make out a face, it was like a very dense fog), I slowly walked up to it until I was standing right before it, looking up at it. It then disappeared. I stuck my hand right where it had been, but there was nothing there.
I continued to see it come up the stairs every morning until we left. My grandmother sold the house and it was torn down, so I never stayed there again or had another opportunity to see this apparition.
Over the years I've come to believe that this was my grandfather. He died before I was born, but I had heard that he was a very gentle and devoted father and husband. I think he was still trying to look after his family.
These days, I have a wife and a two year old. I leave for work at around the same time in the morning that I used to see the ghost all those years ago. I always take one last look at my wife and check in on my son, sometimes kissing his forehead, before I leave. It's just such a comforting and compelling thing for me to do, to know they're both safe and still sleeping. I sometimes wonder whether this is what my grandfather had still been trying to do.
And the fact that it stopped, yes, I can see how it may have been your grandfather.
Then there's the end to your story which demonstrates why you'd believe such, and d'awwwww. Heart. Melting. You are a good husband and father.