Fuji is shy in autumn. I had a room on the north side of Lake Kawaguchi for five nights and the mountain sat behind cloud for four of them. I got up at five each morning anyway and stood by the water with a flask.
It cleared on the fourth morning. The top of the cone came out first, then the rest, and the lake went flat enough to hold the reflection. I had maybe half an hour before the wind picked up and broke the surface.
The other four mornings were not wasted. I know that shoreline well now.