Concept: A sundial where the shadow is cast by a thin plastic string. You can drip water down the plastic string. As water pools throughout the day, the lines become obscured and time becomes harder to read precisely.
The grey base is not part of it, it is just in the photo for visibility.
This is what it looks like with no water yet:
This is the frame:
And below the paper is a mirror.
Maybe, if the paper gets soaked enough one day, it will disintegrate partly and the mirror will reflect a bit of sky. When the mirror shows, the string will not have a shadow.
I wanted my sundial to be imprecise. I got the idea for the water because I imagined if the shadow was cast by a stream of water it would be a wavering shadow. This way you can still get information from the sundial, but it is diluted information. The wavering shadow is not present in my prototype. Perhaps a small clear tube would work to produce this effect.