Create wall from path

I have a model that is using CZML to display 4D flight data. I am able to show the path of the aircraft just fine using:

"path" : {
    "show" : "true",
    "material" : {
        "solidColor" : {
            "color" : {
                "rgba" : [232,232,4,255]
            }
        }
    },
    "width" : 2,
    "leadTime" : 0,
    "trailTime" : 600,
    "resolution" : 20
}

What I would like to be able to do is extrude this path down to the ground. Ideally so that it behaves the same as the path object, appearing only behind the aircraft model and disappearing after a certain amount of time rather than being always on for the whole track.

I've seen some posts that suggest creating a wall object for this, but they seem to render the whole track, not just the bit covered by the path. Can someone please point me to the correct documentation or a working example?

Thanks in advance for your time and help,
Dan