Question: How to color an implicitplot3d?

I have a surface defined by C(x, y, x) = 0 that I visualize with implicitplot3d.
Using shading=shue does not suits me and I would like to define my own coloring function F(x, y, z).

The first error I got made me think that a coloring function cannot depend on 3 parameters.
But a simpler (and not visually satysfying function) F(x, y) already leads to an error, which makes me wonder if it is possible to use a colorig function with  implicitplot3d?

Thanks in advance

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