I'm uncertain exactly what you are after, but maybe you could do this:
Whaen you make your Noise Gradient, for "Color Model" choose HSB, and set the saturation slider to zero, to make it Grayscale. Then, once you have your gradient drawn, add a Gradient Map layer above it, maybe with a gradien similar to this:
You can see the results in the background behind the dialog box here.
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