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I know of only one way to do this. It's making Color Table file from your image and then applying it to target image in Index mode.

It works if you can live with 256 levels of gradient.

Long time ago PS could use Color Table files for Curves which could be used to make your custom gradient. This way you could effectively make Gradient map effect long before it was introduced in PS.

Now PS uses true float values for Color stops and Midpoints in the gradient and doesn't let you use Color Table files in the Curves or Gradient settings at all.